Related papers: Chaos of the logistic equation with piecewise cons…
A R\"ossler model perturbed with a piecewise constant function is investigated. The perturbation function used in the model is constructed by means of the logistic map. In the absence of the perturbation the system is assumed to possess two…
By using the reduction technique to impulsive differential equations [1], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos.…
In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.
Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
In the present study, we investigate the dynamics of impulsive differential equations driven by a chaotic system. We rigorously prove that, likewise the drive, the response impulsive system is also chaotic. Our results are based on the…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
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…
This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorke{\delta}-chaotic if and…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
In this paper, we introduce several new types and generalizations of the concepts distributional chaos and Li-Yorke chaos. We consider the general sequences of binary relations acting between metric spaces, while in a separate section we…
Li-Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained recently. In this note we show that even simpler and more…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points.…
The quasiperiodic route to chaos in a piecewise linear forced parallel LCR circuit with a negative conductance and diode is studied analytically. An explicit analytical solution for the normalized state equations of the piecewise linear…
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…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
We prove the presence of chaos near a homoclinic orbit in the modified Li-Yorke sense [10] by implementing chaotic perturbations. A Duffing oscillator is considered to show the effectiveness of our technique, and simulations that support…
We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period…