Several chaotic properties of cyclic permutation maps are considered. Cyclic refer to p-dimensional dynamical systems the form φ(b1,b2,⋯,bp)=(up(bp),u1(b1),⋯,up−1(bp−1)), where bj∈Hj (j∈{1,2,⋯,p}), p≥2 is an integer, and Hj (j∈{1,2,⋯,p}) compact subintervals real line R=(−∞,+∞). uj:Hj→Hj+1(j=1,2,…,p−1) up:Hp→H1 continuous maps. Necessary sufficient conditions for a class have Li–Yorke chaos, di...

This paper introduces the concept of Kato chaos to linear dynamics and its induced dynamics. investigates some properties for a continuous operator T operators T¯. The main conclusions are as follows: (1) If is accessible, then collection vectors whose orbit has subsequence converging zero residual set. (2) For defined on Fréchet space, equivalent dense Li–Yorke chaos. (3) preserved under itera...

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...

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...

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.

Let π:X→Y be an extension of minimal compact flows such that Rπ≠ΔX. A subflow Rπ is called M-flow if it T.T. and contains a dense set a.p. points. In this paper we mainly prove the following: π PI iff ΔX unique containing in Rπ. If X metric space not PI, then there exists canonical Li-Yorke chaotic particular, Ellis weak-mixing non-proximal non-PI so chaotic. unbounded or non-minimal M-flow, ne...

This paper is concerned with invariance (F1,F2)-scrambled sets under iterations. The main results are an extension of the compound invariance of Li–Yorke chaos and distributional chaos. New definitions of (F1,F2)-scrambled sets in non-autonomous discrete systems are given. For a positive integer k, the properties P(k) and Q(k) of Furstenberg families are introduced. It is shown that, for any po...

In Part I ([9], this journal), Li and McLaughlin proved the existence of homoclinic orbits in certain discrete NLS systems. In this paper, we will construct Smale horseshoes based on the existence of homoclinic orbits in these systems. First, we will construct Smale horseshoes for a general high dimensional dynamical system. As a result, a certain compact, invariant Cantor set3 is constructed. ...

An approach is proposed for making a given stable continuous-time Takagi-Sugeno (TS) fuzzy-system chaotic, by first discretizing it and then using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with posit...