Related papers: Analysis of Chaos and Bifurcation in Nonlinear two…
We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
Chaotic behavior can be produced from difference equations with unstable fixed points. Difference equations can be used for algorithms to control the chaotic behavior by perturbing a system parameter using feedback based on the first…
The chaotic spike train of a homoclinic dynamical system is self-synchronized by re-inserting a small fraction of the delayed output. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…
We consider transitions to chaos in random dynamical systems induced by an increase of noise amplitude. We show how the emergence of chaos (indicated by a positive Lyapunov exponent) in a logistic map with bounded additive noise can be…
We consider the patterns of collective motion emerging when many aligning, self-propelling units move in two dimensions while interacting through a repulsive potential and are also subject to delays and random perturbations. In this…
A simple model of a distributed, non-linear circuit that produces chaos at GHz frequencies is introduced and tested experimentally. The model circuit is a driven diode-terminated transmission line with the transmission line impedance…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during…
The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of…
Chaos is a fundamental phenomenon in nonlinear dynamics, manifesting as irregular and unpredictable behavior across various physical systems. Among the diverse routes to chaos, intermittent chaos is a distinct transition pathway,…
We investigate the interplay of collective and chaotic motion in a classical self-bound N-body system with two-body interactions. This system displays a hierarchy of three well separated time scales that govern the onset of chaos, damping…
A new generic dynamical phenomenon of pseudochaos and its relevance to the statistical physics both modern as well as traditional one are considered and explained in some detail. The pseudochaos is defined as a statistical behavior of the…
What dynamical quantity is actually controlled by higher-order interactions in chaotic oscillator networks remains unclear. In amplitude-active systems, chaos is often interpreted through coherence, yet coherence is not the quantity that…
Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying…
in the last decade, studies of chaotic system are more often used for classical choatic system than for quantum chaotic system, there are many ways of observing the chaotic system such us analyzing the frequency with Fourier transform or…