In this paper Li–Yorke chaotic sets generated by shift and weighted shift maps are studied. The characterization of Li–Yorke chaotic sets by p-scrambled sets, maximal scrambled sets and orbit invariants are proved for the general shift maps. For weighted shift maps on infinite-dimensional spaces, the necessary and sufficient conditions for Li–Yorke chaotic are proved both in the abstract sequen...

The paper analyzes the structure and inner long-term dynamics of invariant compact sets for skewproduct flow induced by a family time-dependent ordinary differential equations nonhomogeneous linear dissipative type. main assumptions are made on term homogeneous equations. rich casuistic includes uniform stability sets, as well presence Li-Yorke chaos Auslander-Yorke inside attractor.

We consider shunting inhibitory cellular neural networks with inputs and outputs that are chaotic in a modified Li-Yorke sense. The original Li-Yorke definition of chaos has been modified such that infinitely many periodic motions separated from the motions of the scrambled set are now replaced with almost periodic ones. Another principal novelty of the paper is that chaos is obtained as soluti...

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×Y, T ×T ) is transitive, then (X, T ) is strongly chaotic in the sense of Li and Yorke. We then show that many of the known sufficient conditions in the literature, as well as a few new results, are corollaries of this statement. In fact the kind of chaotic behavior w...

Let X be a compact metric space, let φ be a continuous self-map on X , and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between various dynamical properties of a given (crisp) dynamical system (X,φ) and its Zadeh’s extension Φ on F(X). Among other things we study various (weak, strong, mild etc.) mixing properties and also s...

Taking advantage of external inputs, it is shown that shunting inhibitory cellular neural networks behave chaotically. The analysis is based on the Li-Yorke definition of chaos. Appropriate illustrations which support the theoretical results are depicted.

In this paper, chaos in a voltage-mode controlled buck converter is studied. The existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of a one-sided shift map, which implies positive entropy of the system and hence chaotic behaviour. The essential tool is the horseshoe hypotheses proposed by Kennedy and...

We first study how to make use of the Marotto theory to prove rigorously the existence of the Li-Yorke chaos in diffusively coupled map lattices with open boundary conditions i.e., a highdimensional discrete dynamical system . Then, the recent 0-1 test for chaos is applied to confirm our theoretical claim. In addition, we control the chaotic motions to a fixed point with delay feedback method. ...