SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 65-93, January 2021. The totally asymmetric simple exclusion process (TASEP) is a basic model of statistical mechanics that has found numerous applications. We consider the case of TASEP with a finite chain where particles may enter from the left and leave to the right at prescribed rates. This model can be formulated as a Markov process

SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 38-64, January 2021. In this article, we aim to classify the dynamic transitions and bifurcations for a family of axisymmetric geophysical fluid problems of a generic fourth-second order structure. A transition theorem is established by reducing the governing partial differential equations to a complex-valued ordinary differential

SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 1-37, January 2021. Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2847-2886, January 2020. Motivated by models that arise in controlled ship maneuvering, we analyze Hopf bifurcations in systems with piecewise smooth nonlinear part. In particular, we derive explicit formulas for the generalization of the first Lyapunov coefficient to this setting. This generically determines the direction of branching

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2829-2846, January 2020. Progression through different synchronized and desynchronized regimes in brain networks has been reported to reflect physiological and behavioral states, such as working memory and attention. Moreover, intracranial recordings of epileptic seizures show a progression towards synchronization as brain regions

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2803-2828, January 2020. A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyze nonlinear dynamical systems brings new strategies for prediction and control, while the approach is straightforward to apply to large

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2783-2802, January 2020. We study the effect of noise on dynamics of a single spike for the classical Gierer--Meinhardt model on a finite interval. When spatio-temporal noise is introduced in the equation for the activator, we derive a stochastic ODE that describes the motion of a single spike on a slow time scale. The steady state

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2749-2782, January 2020. We study a nonlinear wave equation appearing as a model for a membrane (without viscous effects) under the presence of an electrostatic potential with strength $\lambda$. The membrane has a unique stable branch of steady states $u_{\lambda}$ for $\lambda\in\lbrack0,\lambda_{\ast}]$. We prove that the branch

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2737-2748, January 2020. This article studies ordinary differential equations modeling incompressible flow in rigid pipes that connect two distensible vessels, one of which is periodically forced. The forcing controls either the pressure or the volume of the excited vessel and---in part of the period---can be replaced by free relaxation

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2720-2736, January 2020. In this paper we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data into a graph structure and use tools designed for automatic, unsupervised analysis of graphs. Using a few data sets, we show that the collected features of the

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2682-2719, January 2020. Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field limit for a general class of stochastic models representing each individual

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2658-2681, January 2020. This work considers the gravitational $N$-body problem and introduces global time-renormalization functions that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence of the solution to the original equations is derived, which suggests an appropriate

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2628-2657, January 2020. We study distributional solutions to the radially symmetric aggregation equation for power-law potentials. We show that distributions containing spherical shells form part of a basin of attraction in the space of solutions in the sense of “shifting stability." For spherical shell initial data, we prove the

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2594-2627, January 2020. In this paper, we provide a graphic formulation of nonisothermal reaction systems and show that a nonisothermal detailed balanced network system converges (locally) asymptotically to the unique equilibrium within the invariant manifold determined by the initial condition. To model thermal effects, the proposed

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2567-2593, January 2020. We study the dynamics and equilibria induced by training an artificial neural network for regression based on the gradient conjugate prior (GCP) updates. We show that contaminating the training data set by outliers leads to bifurcation of a stable equilibrium from infinity. Furthermore, using the outputs of

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2530-2566, January 2020. We study fast-slow maps obtained by discretization of planar fast-slow systems in continuous time. We focus on describing the so-called delayed loss of stability induced by the slow passage through a singularity in fast-slow systems. This delayed loss of stability can be related to the presence of canard solutions

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2500-2529, January 2020. Motivated by the model proposed by Gandhi et al. in [J. R. Soc. Interface, 15 (2018), 20180508], we propose a two-component reaction-advection-diffusion model for vegetation density and soil water concentration on a curved terrain with elevation given by $z = \zeta(x,y)$ and metric tensor $g(x,y)$. It accounts

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2469-2499, January 2020. In this paper we establish the meta-stability of traveling waves for a class of reaction-diffusion equations forced by a multiplicative noise term. In particular, we show that the phase-tracking technique developed in [C. H. S. Hamster and H. J. Hupkes, SIAM J. Appl. Dyn. Syst., 18, pp. 205--278; Phys. D, 401

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2428-2468, January 2020. Dynamical systems often admit geometric properties that must be taken into account when studying their behavior. We show that many such properties can be encoded by means of quiver representations. These properties include classical symmetry, hidden symmetry, and feedforward structure, as well as subnetwork

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2403-2427, January 2020. Using the Klein--Majda--Damodaran model of nearly parallel vortex filaments, we construct vortex knots and links on a torus involving periodic boundary conditions and analyze their stability. For a special class of vortex knots---toroidal knots---we give a full characterization of both their energetic and dynamical

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2371-2402, January 2020. We discuss tipping phenomena in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp. 275--279]. We give simple testable criteria for the occurrence of nonautonomous tipping from the

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2343-2370, January 2020. Given $p,q\in\mathbb{Z}_{\geq 2}$ with $p\neq q$, we study generalized Abel differential equations $\frac{dx}{d\theta}=A(\theta)x^p+B(\theta)x^q,$ where $A$ and $B$ are trigonometric polynomials of degrees $n, m\ge 1,$ respectively, and we are interested in the number of limit cycles (i.e., isolated periodic

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2322-2342, January 2020. The Kuramoto model is a system of nonlinear differential equations that is often used to model synchronization between coupled oscillators in a network. A particular form of synchronization is phase-locking whereby the oscillators rotate at a common frequency with fixed angle differences. It has been observed

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2286-2321, January 2020. In this paper, we consider a class of quasi-periodically forced reversible systems, obtained as perturbations of a set of harmonic oscillators, and study Stoker's problem (the existence of response solutions) of such systems in the case of Liouvillean frequency. This is based on a finite dimensional Kolmogorov--Arnold--Moser

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2268-2285, January 2020. This note studies 1 and 2 degrees of freedom Hamiltonian systems that are thermostated by a single-variable thermostat. It provides concrete examples of integrable Hamiltonians and single thermostats, including the Nosé--Hoover thermostat, where the existence of a horseshoe in the flow of the thermostated system

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2233-2267, January 2020. We study the classical planar spin-orbit model from an analytical point of view, with no requirements of the smallness of the orbital eccentricity and taking into account dissipative forces. The problem depends on $e$, the eccentricity of the orbit, and on $\Lambda$, the oblateness of the spinning body. Our

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 2194-2231, January 2020. We rigorously prove the existence of traveling fronts in neural field models with lateral inhibition coupling types and smooth sigmoidal firing rates. With Heaviside firing rates as our base point (where unique traveling fronts exist), we repeatedly apply the implicit function theorem in Banach spaces to provide

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 2162-2193, January 2020. In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation via dynamic mode decomposition, a quantization approach was recently

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 2135-2161, January 2020. The ability of a circadian system to entrain to the 24-hour light-dark cycle is one of its most important properties. A new tool, called the entrainment map, was recently introduced to study this process for a single oscillator. Here we generalize the map to study the effects of light-dark forcing in a hierarchical

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 2103-2134, January 2020. In this paper, we study an agent-based interacting particle system with attractive and singular repulsive forces. We prove the collision avoidance between particles from different groups due to repulsive forces. Moreover, we provide a sufficient condition for the emergence of asymptotic consensus in the same

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 2059-2102, January 2020. In this paper, we revisit the folded node and the bifurcations of secondary canards at resonances $\mu\in \mathbb N$. In particular, we prove for the first time that pitchfork bifurcations occur at all even values of $\mu$. Our approach relies on a time-reversible version of the Melnikov approach in [M. Wechselberger

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 2030-2058, January 2020. Spatially localized two-dimensional spot patterns occur for a wide variety of two component reaction-diffusion systems in the singular limit of a large diffusivity ratio. Such localized, far-from-equilibrium patterns are known to exhibit a wide range of different instabilities such as breathing oscillations

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1993-2029, January 2020. Permanent charge is the major structural quantity of an ion channel. It defines the ion channel and its interaction with boundary conditions plays the predominate role for ionic flow properties or functions of the ion channel. In this work, we investigate effects of large magnitude permanent charges of a simple

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1956-1992, January 2020. This article proposes a framework which allows the study of stability robustness of equilibria of a nonlinear system in the face of parametric uncertainties from the point of view of bifurcation theory. In this context, a branch of equilibria is stable if bifurcations (i.e., qualitative changes of the steady-state

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1920-1955, January 2020. Dynamic mode decomposition (DMD) is a data-driven method that models high-dimensional time series as a sum of spatiotemporal modes, where the temporal modes are constrained by linear dynamics. For nonlinear dynamical systems exhibiting strongly coherent structures, DMD can be a useful approximation to extract

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1884-1919, January 2020. To make decisions we are guided by the evidence we collect and the opinions of friends and neighbors. How do we combine our private beliefs with information we obtain from our social network? To understand the strategies humans use to do so, it is useful to compare them to observers that optimally integrate

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1865-1883, January 2020. We study a thermomechanical system comprising an alpha Stirling engine and a flywheel from the perspective of dynamical systems theory. Thermodynamics establishes a static relation between the flywheel's angle and the forces exerted by the two power pistons that constitute the engine. Mechanics, in turn, provides

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1823-1864, January 2020. We study a convex optimization framework for bounding extreme events in nonlinear dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs). This framework bounds from above the largest value of an observable along trajectories that start from a chosen set and evolve over a finite

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1798-1822, January 2020. An important dynamical property of biological interaction networks is persistence, which intuitively means that “no species goes extinct." It has been conjectured that dynamical system models of weakly reversible networks (i.e., networks for which each reaction is part of a cycle) are persistent. The property

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1758-1797, January 2020. We consider a linearly unstable standing wave solution of a parabolic partial differential equation (PDE) on the real line and develop a high order method for polynomial approximation of the local unstable manifold. The unstable manifold describes the breakdown of the nonlinear wave after the loss of stability

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1736-1757, January 2020. Many civilizations have risen and then collapsed. There can be many causes. A major influence can be how Elite (wealthy or ruling) populations interact with the Commoners (workers) and with the environment. Each population's size can fluctuate. We say a model is “Elite-dominated" when the Elites' per capita

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1701-1735, January 2020. Early afterdepolarizations (EADs) are pathological voltage fluctuations that can occur in cardiac cells and are a potent source of potentially fatal arrhythmias. Recent works examining the mechanisms underlying EADs in minimal computational cardiac models have revealed that voltage-driven EADs are canard-induced

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1659-1700, January 2020. Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular way to reveal this essential macroscopic evolution. To compute coherent sets from an aperiodic time-dependent

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1633-1658, January 2020. We propose a computational method (with acronym ALDI) for sampling from a given target distribution based on first-order (overdamped) Langevin dynamics which satisfies the property of affine invariance. The central idea of ALDI is to run an ensemble of particles with their empirical covariance serving as a

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1609-1632, January 2020. The problems of (i) maximizing or minimizing Lagrangian mixing in fluids via the introduction of a spatiotemporally varying control velocity and (ii) globally controlling the finite-time location of trajectories beginning at all initial conditions in a chaotic system are considered. A particular form of solution

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1575-1608, January 2020. Delays are important phenomena arising in a wide variety of real-world systems, including biological ones, because of diffusion/propagation effects or as simplifying modeling elements. We propose here to consider delayed stochastic reaction networks, a class of networks that has received little attention until

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1540-1573, January 2020. We study a model of the cell cycles of a large ensemble of cells that was conceived to explain the coupling between metabolism and the cell cycle observed in cell cycle related, metabolic oscillations in yeast continuous culture. An essential feature of the model is that a negative feedback mechanism robustly

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1525-1539, January 2020. This work deals with the full reduction of the spatial Kepler system for bounded and unbounded motions. Precisely, we consider the four-dimensional oscillator associated to the Kepler system and carry out our program in three stages: axial-axial-energy rather than energy-axial-axial as is customary. This approach

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1496-1524, January 2020. We propose an approach for the synthesis of robust and optimal feedback controllers for nonlinear PDEs. Our approach considers the approximation of infinite-dimensional control systems by a pseudospectral collocation method, leading to high-dimensional nonlinear dynamics. For the reduced-order model, we construct

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1472-1495, January 2020. Pulses in an actively mode-locked laser can occasionally slip relative to the timing signal, leading to fluctuations in the pulse repetition rate. Such events happen rarely, however, making it infeasible to use traditional methods to determine the slip rate. Here, in a model of a soliton-based mode-locked laser

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1438-1471, January 2020. In this paper, we investigate a time-delayed differential model of the transmission dynamics of schistosomiasis with seasonality. In order to study the influence of water temperature on egg hatching into miracidia and the development from miracidia to cercariae, we incorporate time-dependent delays into the

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1392-1437, January 2020. Dengue, zika, and chikungunya are viruses transmitted to humans by Aedes aegypti mosquitoes. In the absence of medical treatments and efficient vaccines, one of the control methods is to introduce Aedes aegypti mosquitoes infected by the bacterium Wolbachia into a population of wild (uninfected) mosquitoes

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1372-1391, January 2020. The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by a partial differential equation, which is also unknown. The input data of the

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1343-1371, January 2020. We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a simple twofold cycle, which is characterized by a closed trajectory

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1312-1342, January 2020. We study emergent behaviors of the Lohe hermitian sphere (LHS) model which is an aggregation model on ${\mathbb C}^d$. The LHS model is a complex analogue of the Lohe sphere model on ${\mathbb R}^d$, and hermitian spheres are invariant sets for the LHS dynamics. For the derivation of the LHS model, we use a

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1291-1311, January 2020. We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bistable cases, we prove the first sharp quantitative estimate on the (sharp) threshold values. Furthermore, numerical explorations

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1271-1290, January 2020. Motivated by the recent works on the stability of symmetric periodic orbits of the elliptic Sitnikov problem, for time-periodic Newtonian equations with symmetries, we will study symmetric periodic solutions which emanated from nonconstant periodic solutions of autonomous equations. By using the theory of Hill's

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1225-1270, January 2020. We study emergent behaviors of the swarm sphere model under attractive-repulsive couplings and present several sufficient frameworks leading to the complete and practical bicluster aggregations using two key ingredients (two-point correlation function and order parameter). From the modeling perspective, we

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1200-1224, January 2020. We develop a definition of rate-induced tipping (R-tipping) in discrete-time dynamical systems (maps) and prove results giving conditions under which R-tipping will or will not happen. Specifically, we study (possibly noninvertible) maps with a time-varying parameter subject to a parameter shift. We show that

SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1160-1199, January 2020. The dynamic mode decomposition (DMD) extracted dynamic modes are the nonorthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis, the extracted dynamic modes are a generalization of global stability