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Learning Bilinear Models of Actuated Koopman Generators from Partially Observed Trajectories SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-03-14 Samuel Otto, Sebastian Peitz, Clarence Rowley
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 885-923, March 2024. Abstract.Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well known that the Koopman generators for control-affine systems also
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Diversity of Emergent Dynamics in Competitive Threshold-Linear Networks SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-03-13 Katherine Morrison, Anda Degeratu, Vladimir Itskov, Carina Curto
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 855-884, March 2024. Abstract.Threshold-linear networks consist of simple units interacting in the presence of a threshold nonlinearity. Competitive threshold-linear networks have long been known to exhibit multistability, where the activity of the network settles into one of potentially many steady states. In this work, we find conditions
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A Computational Approach to Polynomial Conservation Laws SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-03-12 Aurélien Desoeuvres, Alexandru Iosif, Christoph Lüders, Ovidiu Radulescu, Hamid Rahkooy, Matthias Seiß, Thomas Sturm
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 813-854, March 2024. Abstract.For polynomial ODE models, we introduce and discuss the concepts of exact and approximate conservation laws, which are the first integrals of the full and truncated sets of ODEs. For fast-slow systems, truncated ODEs describe the fast dynamics. We define compatibility classes as subsets of the state space
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Preserving Bifurcations through Moment Closures SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-03-12 Christian Kuehn, Jan Mölter
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 791-812, March 2024. Abstract.Moment systems arise in a wide range of contexts and applications, e.g., in network modeling of complex systems. Since moment systems consist of a high or even infinite number of coupled equations, an indispensable step in obtaining a low-dimensional representation that is amenable to further analysis
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Guarantees for Spontaneous Synchronization on Random Geometric Graphs SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-03-07 Pedro Abdalla, Afonso S. Bandeira, Clara Invernizzi
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 779-790, March 2024. Abstract. The Kuramoto model is a classical mathematical model in the field of nonlinear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network’s topology and whether the oscillators synchronize is a central question
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Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross–Pitaevskii Equation with Temporally and Spatially Modulated Coefficients SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-02-28 Haotian Wang, Hujiang Yang, Xiankui Meng, Ye Tian, Wenjun Liu
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 748-778, March 2024. Abstract. This paper studies the soliton dynamics for the Rabi-coupled Gross–Pitaevskii model in multicomponent Bose–Einstein condensates. The model has variable nonlinearities and external potentials and is used to construct a complex multisoliton in an explicit form. The variable nonlinearity and external potential
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Wave-Pinned Patterns for Cell Polarity—A Catastrophe Theory Explanation SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-02-26 Fahad Al Saadi, Alan Champneys, Mike R. Jeffrey
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 721-747, March 2024. Abstract.A class of four-component reaction-diffusion systems are studied in one spatial dimension, with one of four specific reaction kinetics. Models of this type seek to capture the interaction between active and inactive forms of two G-proteins, known as ROPs in plants, thought to underly cellular polarity
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Evolution of Dispersal in Advective Patchy Environments with Varying Drift Rates SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-02-21 Shanshan Chen, Jie Liu, Yixiang Wu
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 696-720, March 2024. Abstract.In this paper, we study a two stream species Lotka–Volterra competition patch model with the patches aligned along a line. The two species are supposed to be identical except for the diffusion rates. For each species, the diffusion rates between patches are the same, while the drift rates vary. Our results
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[math]-Reduction, Relative Equilibria, and Bifurcations for the Full Averaged Model of Two Interacting Rigid Bodies SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-02-21 F. Crespo, D. E. Espejo, J. C. van der Meer
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 668-695, March 2024. Abstract.We present a geometrical description of the symmetries and reduction of the full gravitational 2-body problem after complete averaging over fast angles. Our variables allow for a well-suited formulation in action-angle type coordinates associated with the averaged angles, which provide geometric insight
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Spatio-temporal Dynamics in a Reaction-Diffusion Equation with Nonlocal Spatial Memory SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-02-21 Shuyang Xue, Yongli Song, Hao Wang
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 641-667, March 2024. Abstract.To model a single-species cognitive movement, we formulate a reaction-diffusion equation with nonlocal spatial memory and investigate its dynamics. We explore the influence of the perceptual scale on the stability and Turing bifurcation. When the random diffusion is dominant, the perceptual scale does
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Connecting Anti-integrability to Attractors for Three-Dimensional Quadratic Diffeomorphisms SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-02-06 Amanda E. Hampton, James D. Meiss
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 616-640, March 2024. Abstract. We previously showed that three-dimensional quadratic diffeomorphisms have anti-integrable (AI) limits that correspond to a quadratic correspondence, a pair of one-dimensional maps. At the AI limit the dynamics is conjugate to a full shift on two symbols. Here we consider a more general AI limit, allowing
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A Unified Approach to Reverse Engineering and Data Selection for Unique Network Identification SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-02-05 Alan Veliz-Cuba, Vanessa Newsome-Slade, Elena S. Dimitrova
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 592-615, March 2024. Abstract.Due to cost concerns, it is optimal to gain insight into the connectivity of biological and other networks using as few experiments as possible. Data selection for unique network connectivity identification has been an open problem since the introduction of algebraic methods for reverse engineering for
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Bifurcation Analysis of Bogdanov–Takens Bifurcations in Delay Differential Equations SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-30 M. M. Bosschaert, Yu. A. Kuznetsov
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 553-591, March 2024. Abstract. In this paper, we will perform the parameter-dependent center manifold reduction near the generic and transcritical codimension two Bogdanov–Takens bifurcation in classical delay differential equations. Using an approximation to the homoclinic solutions derived with a generalized Lindstedt–Poincaré method
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On the Application of Optimal Control Techniques to the Shadowing Approach for Time Averaged Sensitivity Analysis of Chaotic Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-29 Rhys E. Gilbert, Davide Lasagna
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 505-552, March 2024. Abstract. Traditional sensitivity analysis methods fail for chaotic systems due to the unstable characteristics of the linearized equations. To overcome these issues two methods have been developed in the literature, one being the shadowing approach, which results in a minimization problem, and the other being
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Reduced Order Characterization of Nonlinear Oscillations Using an Adaptive Phase-Amplitude Coordinate Framework SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-29 Dan Wilson, Kai Sun
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 470-504, March 2024. Abstract. We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently leveraging phase-amplitude-based reduction strategies, we arrive at
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Discrepancy Modeling Framework: Learning Missing Physics, Modeling Systematic Residuals, and Disambiguating between Deterministic and Random Effects SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-25 Megan R. Ebers, Katherine M. Steele, J. Nathan Kutz
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 440-469, March 2024. Abstract.Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations often result in discrepancies between the model and sensor-based
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Interplay between Normal Forms and Center Manifold Reduction for Homoclinic Predictors near Bogdanov–Takens Bifurcation SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-25 Maikel M. Bosschaert, Yuri A. Kuznetsov
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 410-439, March 2024. Abstract.This paper provides for the first time correct third-order homoclinic predictors in [math]-dimensional ODEs near a generic Bogdanov–Takens bifurcation point, which can be used to start the numerical continuation of the appearing homoclinic orbits. To achieve this, higher-order time approximations to the
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Identifying Nonlinear Dynamics with High Confidence from Sparse Data SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-24 Bogdan Batko, Marcio Gameiro, Ying Hung, William Kalies, Konstantin Mischaikow, Ewerton Vieira
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 383-409, March 2024. Abstract.We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More precisely, the sparse data is used to construct a statistical surrogate
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Convergence and Approximation of Invariant Measures for Neural Field Lattice Models under Noise Perturbation SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-24 Tomas Caraballo, Zhang Chen, Lingyu Li
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 358-382, March 2024. Abstract. This paper is mainly concerned with limiting behaviors of invariant measures for neural field lattice models in a random environment. First of all, we consider the convergence relation of invariant measures between the stochastic neural field lattice model and the corresponding deterministic model in
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Sufficient Conditions for Linear Stability of Complex-Balanced Equilibria in Generalized Mass-Action Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-22 Stefan Müller, Georg Regensburger
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 325-357, March 2024. Abstract. Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics and engineering can be written in this form. Previous results
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Shifting Consensus in a Biased Compromise Model SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-22 Olivia Cannon, Ty Bondurant, Malindi Whyte, Arnd Scheel
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 297-324, March 2024. Abstract. We investigate the effect of bias on the formation and dynamics of opinion clusters in the bounded confidence model. For weak bias, we quantify the change in average opinion and potential dispersion and decrease in cluster size. For nonlinear bias modeling self-incitement, we establish coherent drifting
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Reduction of Chemical Reaction Networks with Approximate Conservation Laws SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-19 Aurélien Desoeuvres, Alexandru Iosif, Christoph Lüders, Ovidiu Radulescu, Hamid Rahkooy, Matthias Seiß, Thomas Sturm
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 256-296, March 2024. Abstract. Model reduction of fast-slow chemical reaction networks based on the quasi-steady state approximation fails when the fast subsystem has first integrals. We call these first integrals approximate conservation laws. In order to define fast subsystems and identify approximate conservation laws, we use ideas
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High-Dimensional Cointegration and Kuramoto Inspired Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-18 Jacob Stærk-Østergaard, Anders Rahbek, Susanne Ditlevsen
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 236-255, March 2024. Abstract. This paper presents a novel estimator for a nonstandard restriction to both symmetry and low rank in the context of high-dimensional cointegrated processes. Furthermore, we discuss rank estimation for high-dimensional cointegrated processes by restricted bootstrapping of the Gaussian innovations. We demonstrate
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Dynamics on Hepatitis B Virus Infection In Vivo with Interval Delay SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-17 Haonan Zhong, Kaifa Wang
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 205-235, March 2024. Abstract.In view of the molecular biological mechanism of the cytotoxic T lymphocytes proliferation induced by hepatitis B virus infection in vivo, a novel dynamical model with interval delay is proposed. The interval delay is determined by two delay parameters, namely delay center and delay radius. We derive the
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Stable Synchronous Propagation of Signals by Feedforward Networks SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-16 Ian Stewart, David Wood
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 167-204, March 2024. Abstract.We analyze the dynamics of networks in which a central pattern generator (CPG) transmits signals along one or more feedforward chains in a synchronous or phase-synchronous manner. Such propagating signals are common in biology, especially in locomotion and peristalsis, and are of interest for continuum
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Flow Map Parameterization Methods for Invariant Tori in Quasi-Periodic Hamiltonian Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-12 Álvaro Fernández-Mora, Alex Haro, J. M. Mondelo
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 127-166, March 2024. Abstract. The aim of this paper is to present a method to compute parameterizations of partially hyperbolic invariant tori and their invariant bundles in nonautonomous quasi-periodic Hamiltonian systems. We generalize flow map parameterization methods to the quasi-periodic setting. To this end, we introduce the
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Semianalytical Computation of Heteroclinic Connections Between Center Manifolds with the Parameterization Method SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-04 Miquel Barcelona, Alex Haro, Josep-Maria Mondelo
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 98-126, March 2024. Abstract. This paper presents a methodology for the computation of whole sets of heteroclinic connections between isoenergetic slices of center manifolds of center [math] center [math] saddle fixed points of autonomous Hamiltonian systems. It involves (a) computing Taylor expansions of the center-unstable and center-stable
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Computing Connection Matrices via Persistence-Like Reductions SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-04 Tamal K. Dey, Michał Lipiński, Marian Mrozek, Ryan Slechta
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 81-97, March 2024. Abstract. Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the context of a rapidly growing data science that requires new mathematical
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Spreading and Structural Balance on Signed Networks SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-04 Yu Tian, Renaud Lambiotte
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 50-80, March 2024. Abstract. Two competing types of interactions often play an important part in shaping system behavior, such as activatory and inhibitory functions in biological systems. Hence, signed networks, where each connection can be either positive or negative, have become popular models over recent years. However, the primary
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Truncation of Contact Defects in Reaction-Diffusion Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-03 Milen Ivanov, Björn Sandstede
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 26-49, March 2024. Abstract. Contact defects are time-periodic patterns in one space dimension that resemble spatially homogeneous oscillations with a defect embedded in their core region. For theoretical and numerical purposes, it is important to understand whether these defects persist when the domain is truncated to large spatial
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The Effects of Delay on the HKB Model of Human Motor Coordination SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2024-01-03 L. I. Allen, T. G. Molnár, Z. Dombóvári, S. J. Hogan
SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 1-25, March 2024. Abstract. In this paper, we analyze the celebrated Haken–Kelso–Bunz model, describing the dynamics of bimanual coordination, in the presence of delay. We study the linear dynamics, stability, nonlinear behavior, and bifurcations of this model by both theoretical and numerical analysis. We calculate in-phase and antiphase
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Stability of the Nonwandering Set in the Region of Attraction Boundary under Perturbations with Application to Vulnerability Assessment SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-12-07 Michael W. Fisher, Ian A. Hiskens
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3390-3430, December 2023. Abstract. For many engineered systems it is important to assess vulnerability to potential disturbances in order to ensure reliable operation. Whether the system will recover from a particular finite-time disturbance to a desired stable equilibrium point depends on uncertain and time-varying system parameter
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The Rocking Can: A Reduced Equation of Motion and a Matched Asymptotic Solution SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-12-06 B. W. Collins, C. L. Hall, S. J. Hogan
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3358-3389, December 2023. Abstract. The rocking can problem [M. Srinivasan and A. Ruina, Phys. Rev. E, 78 (2008), 066609] consists of an empty drinks can standing upright on a horizontal plane which, when tipped back to a single contact point and released, rocks down towards the flat and level state. At the bottom of the motion, the
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Bifurcation of Limit Cycles from Boundary Equilibria in Impacting Hybrid Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-12-06 Hong Tang, Alan Champneys
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3320-3357, December 2023. Abstract. A semianalytical method is derived for finding the existence and stability of single-impact periodic orbits born in a boundary equilibrium bifurcation in a general [math]-dimensional impacting hybrid system. Known results are reproduced for planar systems and general formulae derived for three-dimensional
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Symplectic Methods in the Numerical Search of Orbits in Real-Life Planetary Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-12-05 Urs Frauenfelder, Dayung Koh, Agustin Moreno
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3284-3319, December 2023. Abstract. The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g., the three-body problem). The main directions pursued in this article are as follows: (1) given
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Kuramoto Networks with Infinitely Many Stable Equilibria SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-11-30 Davide Sclosa
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3267-3283, December 2023. Abstract. We prove that the Kuramoto model on a graph can contain infinitely many nonequivalent stable equilibria. More precisely, we prove that for every [math] there is a connected graph such that the set of stable equilibria contains a manifold of dimension [math]. In particular, we solve a conjecture of
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Quantifying Different Modeling Frameworks Using Topological Data Analysis: A Case Study with Zebrafish Patterns SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-11-29 Electa Cleveland, Angela Zhu, Björn Sandstede, Alexandria Volkening
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3233-3266, December 2023. Abstract. Mathematical models come in many forms across biological applications. In the case of complex, spatial dynamics and pattern formation, stochastic models also face two main challenges: pattern data are largely qualitative, and model realizations may vary significantly. Together these issues make it
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Centrality-Based Traffic Restriction in Delayed Epidemic Networks SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-11-28 Atefe Darabi, Milad Siami
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3165-3207, December 2023. Abstract. In an epidemic network, lags due to travel time between populations, latent period, and recovery period can significantly change the epidemic behavior and result in successive echoing waves of the spread between various population clusters. Moreover, external shocks to a given population can propagate
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Deep Linear Networks for Matrix Completion—an Infinite Depth Limit SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-11-28 Nadav Cohen, Govind Menon, Zsolt Veraszto
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3208-3232, December 2023. Abstract.The deep linear network (DLN) is a model for implicit regularization in gradient based optimization of overparametrized learning architectures. Training the DLN corresponds to a Riemannian gradient flow, where the Riemannian metric is defined by the architecture of the network and the loss function
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Low-Order Parametric State-Space Modeling of MIMO Systems in the Loewner Framework SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-11-17 Tea Vojkovic, David Quero, Charles Poussot-Vassal, Pierre Vuillemin
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3130-3164, December 2023. Abstract.In this work, we present a novel data-driven method for identifying parametric MIMO generalized state-space or descriptor systems of low order that accurately capture the frequency and time domain behavior of large-scale linear dynamical systems. The low-order parametric descriptor systems are identified
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Numerical Computation of Transverse Homoclinic Orbits for Periodic Solutions of Delay Differential Equations SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-11-16 Olivier Hénot, Jean-Philippe Lessard, Jason D. Mireles James
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3093-3129, December 2023. Abstract. We present a computational method for studying transverse homoclinic orbits for periodic solutions of delay differential equations, a phenomenon that we refer to as the Poincaré scenario. The strategy is geometric in nature and consists of viewing the connection as the zero of a nonlinear map, such
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Spectral Properties of Pullback Operators on Vector Bundles of a Dynamical System SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-11-09 Allan M. Avila, Igor Mezić
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3059-3092, December 2023. Abstract. The spectrum of the Koopman operator has been shown to encode many important statistical and geometric properties of a dynamical system. In this work, we consider induced linear operators acting on the space of sections of the state space’s tangent, cotangent, and tensor bundles. We first demonstrate
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Mitigating Model Error via a Multimodel Method and Application to Tropical Intraseasonal Oscillations SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-11-03 Jason L. Torchinsky, Samuel Stechmann
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3025-3058, December 2023. Abstract. Developing a model to capture all aspects of a complex dynamical system is an immense task, and each model will have deficiencies in some areas, such as global climate models having difficulty in capturing tropical intraseasonal variability such as the Madden–Julian oscillation. Besides complex models
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Rate-Induced Tipping in Heterogeneous Reaction-Diffusion Systems: An Invariant Manifold Framework and Geographically Shifting Ecosystems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-30 Cris R. Hasan, Ruaidhrí Mac Cárthaigh, Sebastian Wieczorek
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2991-3024, December 2023. Abstract. We propose a framework to study tipping points in reaction-diffusion equations (RDEs) in one spatial dimension, where the reaction term decays in space (asymptotically homogeneous) and varies linearly with time (nonautonomous) due to an external input. A compactification of the moving-frame coordinate
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Modeling Polarity-Driven Laminar Patterns in Bilayer Tissues with Mixed Signaling Mechanisms SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-16 Joshua W. Moore, Trevor C. Dale, Thomas E. Woolley
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2945-2990, December 2023. Abstract. Recent advances in high-resolution experimental methods have highlighted the significance of cell signal pathway crosstalk and localized signaling activity in the development and disease of numerous biological systems. The investigation of multiple signal pathways often introduces different methods
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An Unstructured Mesh Approach to Nonlinear Noise Reduction for Coupled Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-13 Aaron Kirtland, Jonah Botvinick-Greenhouse, Marianne DeBrito, Megan Osborne, Casey Johnson, Robert S. Martin, Samuel J. Araki, Daniel Q. Eckhardt
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2927-2944, December 2023. Abstract. To address noise inherent in electronic data acquisition systems and real-world sources, Araki et al. [Phys. D, 417 (2021), 132819] demonstrated a grid-based nonlinear technique to remove noise from a chaotic signal, leveraging a clean high-fidelity signal from the same dynamical system and ensemble
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Regression-Based Projection for Learning Mori–Zwanzig Operators SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-13 Yen Ting Lin, Yifeng Tian, Danny Perez, Daniel Livescu
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2890-2926, December 2023. Abstract. We propose to adopt statistical regression as the projection operator to enable data-driven learning of the operators in the Mori–Zwanzig formalism. We present a principled method to extract the Markov and memory operators for any regression models. We show that the choice of linear regression results
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Equilibria Analysis of a Networked Bivirus Epidemic Model Using Poincaré–Hopf and Manifold Theory SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-12 Brian D. O. Anderson, Mengbin Ye
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2856-2889, December 2023. Abstract. This paper considers a deterministic susceptible-infected-susceptible (SIS) networked bivirus epidemic model (termed the bivirus model for short), in which two competing viruses spread through a set of populations (nodes) connected by two graphs, which may be different if the two viruses have different
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Generalized Eigenvalues of the Perron–Frobenius Operators of Symbolic Dynamical Systems SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-12 Hayato Chiba, Masahiro Ikeda, Isao Ishikawa
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2825-2855, December 2023. Abstract. The generalized spectral theory is an effective approach to analyze a linear operator on a Hilbert space [math] with a continuous spectrum. The generalized spectrum is computed via analytic continuations of the resolvent operators using a dense locally convex subspace [math] of [math] and its dual
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Fast Adjoint Algorithm for Linear Responses of Hyperbolic Chaos SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-12 Angxiu Ni
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2792-2824, December 2023. Abstract. We develop an algorithm for the equivariant divergence formula of the unstable perturbation of unstable transfer operators, by progressively computing [math] many bounded vectors or covectors on one orbit, where [math] is the unstable dimension. Combining this with the nonintrusive adjoint shadowing
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Optimal Control of the Controlled Lotka–Volterra Equations with Applications. The Permanent Case SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-11 Bernard Bonnard, Jérémy Rouot
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2761-2791, December 2023. Abstract. Motivated by the control of complex microbiota for reducing infection by a pathogenic agent, we introduce the theoretical framework from optimal control to analyze this problem. Two complementary approaches can be applied in the analysis: one is the so-called permanent case, where no digital constraints
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Stability of Equilibrium Points in the Spatially Restricted [math]-Body Problem with Manev Potential SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-11 Mauricio Ascencio, Esther Barrabés, Josep M. Cors, Claudio Vidal
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2732-2760, December 2023. Abstract. We study the dynamics of an infinitesimal mass under the gravitational attraction of [math] primaries arranged in a planar ring configuration plus the influence of the central mass with a Manev potential [math], [math], where [math] is a parameter related to the oblaticity or radiation source (according
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Organization of Spatially Localized Structures near a Codimension-Three Cusp-Turing Bifurcation SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-10 Pedro Parra-Rivas, Alan R. Champneys, Fahad Al Saadi, Damia Gomila, Edgar Knobloch
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2693-2731, December 2023. Abstract. A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial interactions. This work provides a generic unfolding in one spatial dimension of a certain codimension-three singularity
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Critical Transitions in d-Concave Nonautonomous Scalar Ordinary Differential Equations Appearing in Population Dynamics SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-10-10 Jesús Dueñas, Carmen Núñez, Rafael Obaya
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 2649-2692, December 2023. Abstract. A function with finite asymptotic limits gives rise to a transition equation between a “past system” and a “future system.” This question is analyzed in the case of nonautonomous coercive nonlinear scalar ordinary differential equations with concave derivative with respect to the state variable.
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Non-Markovian Models of Opinion Dynamics on Temporal Networks SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-09-06 Weiqi Chu, Mason A. Porter
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 3, Page 2624-2647, September 2023. Abstract. Traditional models of opinion dynamics, in which the nodes of a network change their opinions based on their interactions with neighboring nodes, consider how opinions evolve either on time-independent networks or on temporal networks with edges that follow Poisson statistics. Most such models are
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Data-Driven Discovery of Governing Equations for Coarse-Grained Heterogeneous Network Dynamics SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-09-06 Katherine Owens, J. Nathan Kutz
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 3, Page 2601-2623, September 2023. Abstract. We leverage data-driven model discovery methods to determine governing equations for the emergent behavior of heterogeneous networked dynamical systems. Specifically, we consider networks of coupled nonlinear oscillators whose collective behavior approaches a limit cycle. Stable limit cycles are
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Abundance of Infinite Switching SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-08-30 Alexandre A. P. Rodrigues, Luisa Castro
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 3, Page 2570-2600, September 2023. Abstract. We describe a class of vector fields exhibiting abundant switching near a heteroclinic network: for every neighborhood of the network and every infinite admissible path, the set of initial conditions within the neighborhood that follows the path has positive Lebesgue measure. The proof relies on
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Stability Analysis of the Immune System Induced by Chemotaxis SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-08-24 Pan Zheng, Wenhai Shan, Guangyuan Liao
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 3, Page 2527-2569, September 2023. Abstract. This paper investigates the stability and instability of a generalized reaction-diffusion-advection system, which describes a cross-talk between antigens and immune cells via chemokines in the immune system. Based on the spectral analysis, energy estimates, and bootstrap techniques, we first consider
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Rotating Shallow Water Equations with Bottom Drag: Bifurcations and Growth Due to Kinetic Energy Backscatter SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-08-23 Artur Prugger, Jens D. M. Rademacher, Jichen Yang
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 3, Page 2490-2526, September 2023. Abstract. The rotating shallow water equations with f-plane approximation and nonlinear bottom drag are a prototypical model for midlatitude geophysical flow that experience energy loss through simple topography. Motivated by numerical schemes for large-scale geophysical flow, we consider this model on the
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Hopf Bifurcations of Reaction Networks with Zero-One Stoichiometric Coefficients SIAM J. Appl. Dyn. Syst. (IF 2.1) Pub Date : 2023-08-17 Xiaoxian Tang, Kaizhang Wang
SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 3, Page 2459-2489, September 2023. Abstract. For reaction networks with zero-one stoichiometric coefficients (or simply zero-one networks), we prove that if a network admits a Hopf bifurcation, then the rank of the stoichiometric matrix is at least four. As a corollary, we show that if a zero-one network admits a Hopf bifurcation, then it