Abstract This paper is concerned with the existence of chaos for a type partial difference equations. We establish four chaotification schemes equations tangent and cotangent functions, in which systems are shown to be chaotic sense Li–Yorke or both Devaney. For illustration, we provide three examples provided.

James Yorke won the 2003 Japan Prize for his work in the field of chaos theory. This book was compiled by four of his best-known collaborators in honor of his 60th birthday and contains papers by various authors on chaos and chaotic attractors. The papers are organized around the topics of “natural” invariant measure and fractal dimension of the associated chaotic attractors. A few of the paper...

This paper is concerned with anti-control (or, chaotification) of chaos for discrete dynamical systems in general and some special Banach spaces, via feedback control techniques. The controlled systems are proved to be chaotic in the sense of both Devaney and Li-Yorke. The original system can be driven to be chaotic by using an arbitrarily small-amplitude state feedback control in certain Banac...

Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously some regimes. Here we provide formal results for original regime [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049-3052, 1998]. We first construct a trapping region...

Chaos has been successfully applied in many fields to improve the performance of engineering systems, such as communication, vibration compact, and mixing. Generating chaos from originally non-chaotic systems is a relevant topic because potential applications. In this work, impulse control shown generate system. Using Chen system an example, we prove by analytical numerical methods that indeed ...

This paper provides an easily verifiable sufficient condition for topological chaos for unimodal maps which can be satisfied when the well-known Li Yorke condition is not satisfied. It then shows how this result can be applied to a model of endogenous growth with externalities to establish the existence of chaotic equilibrium growth paths in that framework. Journal of Economic Literature Classi...

In this paper, the dynamics of elementary cellular automaton rule 41 is investigated in the bi-infinite symbolic sequence space. In spite of rule 41 is not surjective, but it possess of rich and complex dynamical behaviors. The existence of attractors and subshifts of finite type of the rule’s global map is strictly proved, some interesting dynamical properties on these subshifts, such as posit...

In the present study, dynamics of retarded shunting inhibitory cellular neural networks (SICNNs) is investigated with Li–Yorke chaotic external inputs and outputs. Within the scope of our results, we prove the presence of generalized synchronization in coupled retarded SICNNs, and confirm it by means of the auxiliary system approach. We have obtained more than just synchronization, as it is pro...