Related papers: Bifurcations and Chaos in Time Delayed Piecewise L…
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially…
This study examines the dynamical properties of the Ikeda map, with a focus on bifurcations and chaotic behavior. We investigate how variations in dissipation parameters influence the system, uncovering shrimp-shaped structures that…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
This work deals with bifurcation and the chaotic behavior in one dimensional chains of small particles. We consider two distinct possibilities, one where the particles are modeled by a fourth-order potential which was already studied. We…
We prove that for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
The objective of this paper is to investigate the stability of limit cycles of a mathematical model with a distributed delay which describes the interaction between p53 and mdm2. Choosing the delay as a bifurcation parameter we study the…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The…
This paper investigates the stability of different regions in the $(k,\gamma)$-plane for a class of fractional delay differential equations given by \begin{equation} D^{\alpha} x(t) = -\gamma x(t) + g\big(x(t - \tau_1)\big) - e^{-\gamma…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
The dynamics of two nonlinear Bloch systems is studied from the viewpoint of bifur- cation and a particular parameter space has been explored for the stability analysis based on stability criterion. This enables the choice of the desired…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
In this paper a stability analysis for a Cournot duopoly model with tax evasion and time-delay in a continuous-time framework is presented. The mathematical model under consideration follows a gradient dynamics approach, is nonlinear and…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
For the fractional order systems \[D^\alpha x(t)=f(x),\quad 0<\alpha\leq 1,\] one can have a critical value of $\alpha$ viz $\alpha_*$ such that the system is stable for $0<\alpha<\alpha_*$ and unstable for $\alpha_*<\alpha\leq 1$. In…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
The finite duration of collisions appear as time-nonlocality in the kinetic equation. Analyzing the corresponding quantum kinetic equation for dense interacting Fermi systems a delay differential equation is obtained which combines time…