Related papers: Bifurcations and Chaos in Time Delayed Piecewise L…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…
Weak chaos in high-dimensional conservative systems can be characterized through sticky effect induced by invariant structures on chaotic trajectories. Suitable quantities for this characterization are the higher cummulants of the finite…
This paper is concerned with strong Li-Yorke chaos induced by A-coupled-expansion for time-varying (i.e., nonautonomous) discrete systems in metric spaces. Some criteria of chaos in the strong sense of Li-Yorke are established via strict…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
We investigate synchronization between two unidirectionally linearly coupled chaotic non-identical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent…
In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of…
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…
In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from delay…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
Defect-chaos is studied numerically in coupled Ginzburg-Landau equations for parametrically driven waves. The motion of the defects is traced in detail yielding their life-times, annihilation partners, and distances traveled. In a regime in…
We introduce a ``spatial'' Lyapunov exponent to characterize the complex behavior of non chaotic but convectively unstable flow systems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that…
Understanding the interplay of order and disorder in chaotic systems is a central challenge in modern quantitative science. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work…