Related papers: Desynchronization bifurcation of coupled nonlinear…
We report on transcritical bifurcations of periodic orbits in non-integrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties using a recent mathematical description of transcritical…
Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…
Nonlinear phononics has emerged as a powerful paradigm for the nonthermal control of quantum materials by engineering a conservative potential energy landscape. Here, we show that dissipation can serve as an additional control knob for…
The global bifurcation diagrams for two different one-parametric perturbations ($+\lambda x$ and $+\lambda x^2$) of a dissipative scalar nonautonomous ordinary differential equation $x'=f(t,x)$ are described assuming that 0 is a constant…
This paper investigates the problem of synchronization for nonlinear systems. Following a Lyapunov approach, we firstly study global synchronization of nonlinear systems in canonical control form with both distributed…
This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the…
We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic…
This paper investigates the dynamical system governing the phase differences between three identical oscillators arranged symmetrically and coupled by burst interactions. By constructing a discrete Lyapunov function, we prove the existence…
We consider a three-dimensional chaotic system consisting of the suspension of Arnold's cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a synchronization phenomenon, in the sense…
Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires…
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
We obtain sufficient conditions for the stability of the synchronized solutions for a class of coupled dynamical systems. This is accomplished by finding an analytical expression for the transverse Liapunov exponent through spectral…
An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context,…
We address the problem of stability of synchronization in two diffu- sively coupled oscillators under small perturations. We have two cases, namely, when the perturation becomes of a linear operator and the case of non-linear operator. We…
In nontwist systems, primary shearless curves act as barriers to chaotic transport. Surprisingly, the onset of secondary shearless curves has been reported in a few twist systems. Meanwhile, we found that, in twist systems, the onset of…
The Ohta-Kawasaki model for diblock copolymers exhibits a rich equilibrium bifurcation structure. Even on one-dimensional base domains the bifurcation set is characterized by high levels of multi-stability and numerous secondary bifurcation…
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,…
A numerical and analytical study was conducted to investigate the bifurcation mechanisms that cause desynchronization between the soliton repetition frequency and the frequency of external pulsed injection in a Kerr cavity described by the…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…