Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that transport the symplectic form into a multiple of itself (with a conformal factor smaller than 1). It is important to understand the structure and the dynamics on the attractors. It is well-known that, with the aid of parameters

In this paper, we develop a new approximation for the generalized fractional derivative, which is characterized by a scale function and a weight function. The new approximation is then used in the numerical treatment of a class of generalized fractional sub-diffusion equations. The theoretical aspects of solvability, stability and convergence are established rigorously in maximum norm by discrete energy

Nonlinear Schrödinger equations play essential roles in different physics and engineering fields. In this paper, a hyper-block finite-difference self-consistent method (HFDSCF) is employed to solve this stationary nonlinear eigenvalue equation and demonstrated its accuracy. By comparing the results with the Sinc self-consistent (SSCF) method and the exact available results, we show that the HFDSCF

From a physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth as expressed by the Lipschitz condition. On the other hand, non-linear local growth conditions have been also proposed in the literature. The manuscript investigates the general properties of the local generalizations of derivatives assuming the usual topology of the real line. The concept of a

This paper presents an effective approach to constructing numerical attractors of a general class of continuous homogenous dynamical systems: decomposing an attractor as a convex combination of a set of other existing attractors. For this purpose, the convergent Parameter Switching (PS) numerical method is used to integrate the underlying dynamical system. The method is built on a convergent fixed

We study the effect of switching the order of administration of cytotoxic drugs and radiation in cancer therapy by comparing a sequential and a concurrent protocol of chemoradiation. For this purpose, we derive a nonlinear ordinary differential equation model based on well-accepted knowledge of chemotherapy and radiotherapy for in vitro solid tumors. Using the bifurcation theory, we demonstrate that

In this study, we develop a new algorithm for online variance components estimation (Online-VCE) of geodetic data based on the batch expectation-maximization (EM) algorithm and stochastic approximation theory. The Online-VCE algorithm is then applied to the Kalman filter and least-squares method and validated using simulated kinematic precise point positioning (PPP) based on the global navigation satellite

This study seeks to understand whether and to what extent High Frequency Trading (HFT) affects the probabilistic properties of the stock returns in five markets. More specifically, it focuses on the impact of HFT/Machine trading on five major stock indices, DAX, Nikkei 225, S&P 500, Russell 2000, and TOPIX. The empirical analysis demonstrates that while the introduction of machine trading and/or HFT

We propose a new method for finding discrete eigenvalues for the direct Zakharov-Shabat problem, based on moving in the complex plane along the argument jumps of the function a(ζ), the localization of which does not require great accuracy. It allows to find all discrete eigenvalues taking into account their multiplicity faster than matrix methods and contour integrals. The method shows significant

In this article, we construct the approximate solutions to the Euler-Poisson system in an annular domain, that arises in the study of dynamics of plasmas. Due to a small parameter (proportional to the square of the Debye length) multiplied to the Laplacian operator, together with unmatched boundary conditions, we find that the solutions exhibit sharp transition layers near the boundaries, which makes

In this paper we study a design problem to tune the robustness of a membrane by changing its vulnerability. Consider an energy functional corresponding to solutions of Poisson’s equation with Robin boundary conditions. The aim is to find functions in a rearrangement class such that their energies would be a given specific value. We prove that this design problem has a solution and also we propose a

Largely recognized as leading concepts in network traffic prediction, machining or image processing, the processes of auto-duplication, self-organization and auto-replication are highly useful and fascinating for chaos and fractal theorists. Those processes appear naturally around us as observed on trees, river deltas, lightning, growth spirals, flowers, romanesco broccoli, frost, etc. Using mathematical

This paper presents a systematical and algorithmic approach for determining the maximum number of limit cycles of parametric Liénard system that bifurcate from the period annulus of the corresponding Hamiltonian system. We provide an algebraic criterion for the Melnikov function of the considered system to have Chebyshev property. By using this criterion, we reduce the problem of analyzing the Chebyshev

In this work, we investigate numerically Higgs’ boson equation in the de Sitter space-time, which is an important (3+1)-dimensional model arising in particle physics. Associated with this model, there exists a functional of energy which is dissipated with respect to time. Moreover, some relevant solutions of this model present radial symmetry in three spatial dimensions. In this work, we consider a

Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an α-stable Lévy process is still lacking. Here, we propose an approach to infer all the uncertain non-Gaussian parameters and other system parameters by minimizing the Hellinger distance over the parameter space. The

Electrostatic actuation of micro-structures is largely affected by static charges, leading to its unpredictable behavior. Microstructures mainly accumulate static charges during fabrication, handling and operation. Moreover, microstructures are also actuated by charge-voltage combinations to improve its performance, i.e., increasing travel range. In this article, a distributed parameter model of microbeam

Wetlands were long considered a nuisance because they were not suitable for growth of many agriculture products. Nowadays, owing to it’s importance in agriculture engineering, wetlands are invaluable to the mankind. Wetlands due to their commanding influences on ecosystem, benefited people and the environment in terms of water supply, climate regulation, biodiversity conservation and contaminant erosion

Examples of synchronization, pervasive throughout the natural world, are often awe-inspiring because they tend to transcend our intuition. Synchronization in chaotic dynamical systems, of which the Lorenz system is a quintessential example, is even more surprising because the very defining features of chaos include sensitive dependence on initial conditions. It is worth pursuing, then, the question

Fractal-dimensions (D) and Hurst-exponent (H) are often used for determining a randomness (RI) or predictability index in distributed signals, from the linear relationship of RI = 1–H = D–1, as H+D = 2. This paper investigates the similarities and differences of the results of different methods, when calculating D, H, and RI with the same dataset signals. 8 different methods were tested: Higuchi's

Nonlinear grey Bernoulli multivariate model NGBMC (1, n) is known as a novel forecasting model for nonlinear time series with small samples. However, ill-posed problem would make it less efficient and even cause large errors. In order to improve its generality, a hybrid method combining Elastic Net and multi-objective optimization is introduced in this work. This method effectively solves the essential

This paper introduces an extension of the Mikhailov stability criterion to a class of discrete-time noncommensurate fractional-order systems using the nabla fractional-order Grünwald-Letnikov difference. The new stability analysis methods proposed in the paper are computationally simple and can be effectively used both for commensurate and noncommensurate fractional-order systems. The main advantage

In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most methods currently used in mission design rely on using eigenvectors of the linearized dynamics as local approximations of the manifolds. Since such approximations

Bound states in the continuum (BICs) are generally considered unusual phenomena. In this work, first, we provide a method to analyze the spatial structure of particle’s bound states in the presence of a minimal length, which can be used to find BICs; second, we provide a method to analyze the singular perturbation term’s effect of the Schrödinger equation, which can determine whether the BICs are readily

We study the modified Martínez Alonso–Shabat equationuyuxz+αuxuty−(uz+αut)uxy=0and present its recursion operator and an infinite commuting hierarchy of full-fledged nonlocal symmetries. To date such hierarchies were found only for very few integrable systems in more than three independent variables.

Time irreversibility, which characterizes nonequilibrium processes, can be measured based on the probabilistic differences between symmetric vectors. To simplify the quantification of time irreversibility, symmetric permutations instead of symmetric vectors have been employed in some studies. However, although effective in practical applications, this approach is conceptually incorrect. Time irreversibility

The paper contains a rigorous proof of existence of symbolic dynamics chaos in the generalized Hénon map’s 4th iterate H4, which was conjectured in the paper A 3D Smale Horseshoe in a Hyperchaotic Discrete-Time System of Li and Yang, 2007. We prove also the uniform hyperbolicity of the invariant set with symbolic dynamics. The proofs are computer-assisted with the use of C++ library CAPD for interval

The brain has the phenomenal ability to reorganise itself by forming new connections among neurons and by pruning others. The so-called neural or brain plasticity facilitates the modification of brain structure and function over different time scales. Plasticity might occur due to external stimuli received from the environment, during recovery from brain injury, or due to modifications within the body

Sleep timing is based on the interactions between circadian and homeostatic processes. However, sleep deprivation perturbs the time of sleep onset, and the timing and duration of the following recovery sleep may differ from that of baseline sleep. Here we show that the responses to 0–24 h of sleep deprivation can be approximated by a one-dimensional, discontinuous map computed from a physiologically-based

We conduct a rigorous mathematical analysis of an oscillatory behaviour during the capillary flow. Our investigation concerns a nonlinear ODE modelling rise in a narrow vertical tube. This equation has been proposed by many authors as a generalization and improvement over the classical Lucas-Washburn model. The extension includes components related to a non-zero immersion length and to a discontinuous

In order to study the strain rate effect and size effect during the brittle failure process of ice under uniaxial tension and compression with numerical means, particle-subdomain method (PSM) is introduced. PSM is a continuum-discontinuum coupled method with time-dependent explicit algorithm of dynamic relaxation, which has combined the advantages of particle-in-cell method, finite element method and

Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fractional diffusion model with moving boundary i.e. American and barrier option pricing in the subdiffusive Black–Scholes (B–S) model. Two computational methods for valuing American options in the considered model are proposed

In the present work we explore the application of a few root-finding methods to a series of prototypical examples. The methods we consider include: (a) the so-called continuous-time Nesterov (CTN) flow method; (b) a variant thereof referred to as the squared-operator method (SOM); and (c) the joint action of each of the above two methods with the so-called deflation method. More “traditional” methods

The initial value problem for a generalized forced Burgers equation with variable coefficients Ut+(μ˙(t)/μ(t))U+UUx=(1/2μ(t))Uxx−a(t)Ux+b(t)(xU)x−ω2(t)x+f(t),x∈R,t>0, is solved using Cole-Hopf linearization and Wei-Norman Lie algebraic approach for finding the evolution operator of the associated linear diffusion type equation. As a result, solution of the initial value problem is obtained in terms

This paper develops a sparse flocking control for the fractional Cucker–Smale multi-agent model. The Caputo fractional derivative, in the equations describing the dynamics of a consensus parameter, makes it possible to take into account in the self-organization of group its history and memory dependency. External control is designed based on necessary conditions for a local solution to the appropriate

In this paper we propose a Nonlocal Operator Method (NOM) for the solution of the Cahn-Hilliard (CH) equation exploiting the higher order continuity of the NOM. The method is derived based on the method of weighted residuals and implemented in 2D and 3D. Periodic boundary conditions and solid-wall boundary conditions are considered. For these boundary conditions, the highest order in the NOM scheme

A prey-predator model with a sexual reproduction in prey population and nonlocal consumption of resources by prey in two spatial dimensions is considered. Patterns produced by the model without nonlocal terms and periodic boundary conditions are studied first. Then, Turing patterns induced by the nonlocal interaction (see Banerjee et al. (2018) [1]) in the two dimensional space are explored along with

Due to the lack of a discrete fractional Grönwall-type inequality, the techniques of analyzing the L2−1σ difference schemes would not be correct to apply directly to the nonlinear multi-term fractional subdiffusion equations with time delay, especially when the maximum order of the fractional derivatives is not an integer. The purpose of this paper is twofold. First, we introduce a discrete form of

Immunotherapy has the potential to change the way all cancer types are treated and cured. Cancer immunotherapies use elements of the patient immune system to attack tumor cells. One of the most successful types of immunotherapy is CAR-T cells. This treatment works by extracting patient’s T-cells and adding to them an antigen receptor allowing tumor cells to be recognized and targeted. These new cells

In magnetic films driven by spin-polarized currents, the perpendicular-to-plane anisotropy is equivalent to breaking the time translation symmetry, i.e., to a parametric pumping. In this work, we numerically study those current-driven magnets via the Landau–Lifshitz–Gilbert–Slonczewski equation in one spatial dimension. We consider a space-dependent anisotropy field in the parametric-like regime. The

This paper addresses the approximation of solutions to some non-homogeneous boundary value problems associated with the nonlinear Korteweg-de Vries equation (KdV) and a system of two coupled KdV-type equations derived by Gear and Grimshaw posed on a bounded interval. An efficient Galerkin scheme that combines a finite element strategy for space discretization with a second-order implicit scheme for

In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. López-de-la-Cruz and A. Rapaport. A way to model stochastic perturbations in population dynamics models with bounded realizations, Commun Nonlinear Sci Numer Simulat, 77(2019) 239–257]. We present a correct way to model real noisy perturbations by considering a slightly different stochastic process based, as in the original

Assuming accumulated charge being dependent on capacitor voltage memory as well as by expressing magnetic flux in inductor in terms of current memory, generalized capacitor and inductor are constitutively modeled by the sum of terms containing instantaneous and power type hereditary contributions. Constitutive models are further used in analyzing transient and steady state responses of series RLC circuit

The analysis of intracardiac signals, or electrograms (EGM), is one of the most promising tools to guide catheter ablation of atrial fibrillation and improve the success of this procedure. Given the nonlinear nature of EGM signals, several studies have conducted fractal and multifractal analyses to extract nonlinear features related with critical activity. However, the fractal exponent or the multifractal

This article introduces the third generation of an interesting tool created for time-frequency-shape (TFS) joint analysis. Called Discrete Shapelet Transform (DST-III), it improves both its predecessors, i.e., DST-I and DST-II, in such a way that nearly symmetric major shapelet functions, and consequently almost linear-phase filterbanks, are obtained. Following a brief review on important concepts

In this work we assume rational expectations to pose general equilibrium models with heterogeneous firms that can enter or exit the industry. More precisely, we assume a general Ito process for the dynamics of the agents productivity, including the main dynamics in the literature. A Hamilton-Jacobi-Bellman (HJB) formulation models the endogenous decision of firms to remain or exit the industry. All

The rapid adoption of sensors has improved the communication capacity of vehicles, while connected vehicles are expected to become commercially available in the near future. In a connected vehicle environment, the dynamic continuous kinetic information on roadway could be readily available through sensors and internet of vehicular technologies. Nevertheless, in practice the vehicular networks may suffer

We study the coexistence of synchronous as well as asynchronous dynamical behaviours namely chimera states in an ensemble of nonlinear oscillators coupled through different variables. In this system, such states are a result of multistability induced by the coupling in one variable. By tuning the coupling parameter in a different variable, the region of multistability can be shifted. This provides

The concept of quasi-zero-stiffness (QZS) vibration isolator was proposed inrecent decades aiming at improving the low-frequency isolation performance in a passive manner. However, large excitation and small damping usually cause the transmissibility curve to bend seriously to the right, which greatly reduces the effective isolation region. This paper focuses on enhancing the QZS isolator by introducing

In this paper, we study the bifurcation of limit cycles near a heterocilinc loop with hyperbolic saddles in a perturbed planar Hamiltonian system. We present a method for computing the coefficients in the corresponding expansion of the first order Melnikov function. With more those coefficients, more limit cycles could be determined around the heteroclinic loop. An example of studying limit cycles

The relative orbital motion problem of a deputy spacecraft with respect to a chief spacecraft is, generally, described using a set of differential equations governing the motion of the spacecraft relative to each other instead of describing their motion, separately, relative to the Earth. In this paper, new time-varying, time periodic cubic approximation model of spacecraft relative motion is developed

Classical Kramers-Krönig (K–K) relations connect real and imaginary parts of the frequency-domain response of a system. The K–K relations also hold between the logarithm of modulus and the argument of the response, e.g. between the attenuation and the phase shift of a solution to a wave-propagation problem. For square-integrable functions of frequency, the satisfaction of classical K–K relations implies

We study discontinuous differential-algebraic equations (DDAEs) with a co-dimension 1 discontinuity manifold Σ. Our main objectives are to give sufficient conditions that allow to extend the DAE along Σ and, when this is possible, to define sliding motion (the sliding DAE) on Σ, extending Filippov construction to this DAE case. Our approach is to consider discontinuous ODEs associated to the DDAE and

This study derives a nonlinear reduced-order model in order to evaluate the efficacy of an energy harvesting absorber at controlling base excitations, vortex-induced vibrations, and simultaneous base excitations and vortex-induced vibrations. Vibration absorbers are secondary systems that couple with a primary structure to dissipate the mechanical energy of vibrations. An energy harvesting absorber

Complexity-entropy causality plane (CECP) and ordinal transition network (OTN) are both crucial tools to reveal the characteristics of time series and distinguish complex systems. However, when the parameters of the system to be distinguished have a wide range of values, the distinguishing function of CECP is weakened. Therefore, we propose a new measure called transition Fisher information (TFI) based

Complex elastic media such as biological membranes, in particular, blood vessels, may be described as fiber-reinforced solids in the framework of nonlinear hyperelasticity. Finite axially symmetric anti-plane shear displacements in such solids are considered. A general nonlinear wave equation governing such motions is derived. It is shown that in the case of Mooney-Rivlin materials with standard quadratic

This paper investigates the modelling of rigid-flexible coupling effect on the attitude dynamics and spin control of an electric solar wind sail (E-sail) by developing a rigid-flexible coupling dynamic model. The model considers the attitude dynamics of the central spacecraft, the elastic deformation of the tethers and the rigid-flexible coupling between the spacecraft and the tether. The attitude

A generalized Burgers equation with variable coefficients is introduced based on the (2+1)-dimensional Burgers equation. Using the test function method combined with the bilinear form, we obtain the lump solutions to the generalized Burgers equation with variable coefficients. The amplitude and velocity of the extremum point are derived to analyze the propagation of the lump wave. Moreover, we derive

We provide a new effective method for the two-dimensional distributed-order fractional differential equations (DOFDEs). The technique is based on fractional-order Chebyshev wavelets. An exact formula involving regularized beta functions for determining the Riemann-Liouville fractional integral operator of these wavelets is given. The given wavelets and this formula are utilized to find the solutions

The dynamics of discrete-time fractional order control systems depends on the method used for implementing the fractional derivatives and integrals. A reliable numerical approach adopts the generalized mean of the continuous to discrete conversion. The extra freedom provided by the proposed method must be carefully optimized by the user. This paper investigates the use of multidimensional scaling for

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be globally asymptotically stable. They are given in terms of the global attractivity of the fixed point in a limiting interval map. The existence of slowly oscillating