Related papers: Almost Periodicity in Chaos
We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and…
In this paper the chaos persistence in a class of discontinuous dynamical systems of fractional-order is analyzed. To that end, the Initial Value Problem is first transformed, by using the Filippov regularization [1], into a set-valued…
This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control…
Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of…
Transient chaos is an ubiquitous phenomenon characterizing the dynamics of phase space trajectories evolving towards a steady state attractor in physical systems as diverse as fluids, chemical reactions and condensed matter systems. Here we…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
Chaotic iterations have been introduced on the one hand by Chazan, Mi- ranker [6] and Miellou [10] in a numerical analysis context, and on the other hand by Robert [12] and Pellegrin [11] in the discrete dynamical systems frame- work. In…
This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…
Two properties are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems. While most of the attention…
An analytic theory is developed for the density of states oscillations in quantum wells in a magnetic field which is tilted with respect to the barrier planes. The main oscillations are found to come from the simplest one or two-bounce…
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable…
We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $\epsilon$…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
The results of this study are continuation of the research of Poincar\'e chaos initiated in papers (Akhmet M, Fen MO. Commun Nonlinear Sci Numer Simulat 2016;40:1-5; Akhmet M, Fen MO. Turk J Math, doi:10.3906/mat-1603-51, accepted). We…
We analyze the behavior of a relativistic particle moving under the influence of a uniform magnetic field and a stationary electrostatic wave. We work with a set of pulsed waves that allows us to obtain an exact map for the system. We also…
This work theoretically investigates the transition from topology to chaos in a periodically driven system consisting of a quantum top coupled to a spin-1/2 particle. The system is driven by two alternating interaction kicks per period. For…
Let (X,T) be a topologically transitive dynamical system. We show that if there is a subsystem (Y,T) of (X,T) such that (X\times Y, T\times T) is transitive, then (X,T) is strongly chaotic in the sense of Li and Yorke. We then show that…
Dissipation is commonly regarded as an obstacle to quantum control, as it induces decoherence and irreversibility. Here we demonstrate that dissipation can instead be exploited as a resource to reshape the dynamics of interacting quantum…