In the past decade, there have been some studies about control methods with the purpose of either reducing “bad” chaos or introducing “good” chaos [Chen & Dong, 1998]. Due to its great potential in nontraditional applications such as those found within the context of physical, chemical, mechanical, electrical, optical, and particularly, biological and medical systems [Chen et al., 2001; Schiff ...

This paper establishes the existence of endogenous cycles in infinite-horizon open economy models with a flow collateral constraint. It shows that for plausible parameter configurations, has unique equilibrium exhibiting deterministic which periods debt growth are followed by deleveraging. In particular, three-period exist, implies Li-Yorke Theorem presence any periodicity and chaos. The also a...

Title of dissertation: QUASIPERIODICITY AND CHAOS Suddhasattwa Das, Doctor of Philosophy, 2015 Dissertation directed by: Professor James A. Yorke Department of Mathematics In this work, we investigate a property called “multi-chaos” is which a chaotic set has densely many hyperbolic periodic points of unstable dimension k embedded in it, for at least 2 different values of k. We construct a fami...

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...

A relatively small number of mathematically simple maps and flows are routinely used as examples of low-dimensional chaos. These systems typically have a number of parameters that are chosen for historical or other reasons. This paper addresses the question of whether a different choice of these parameters can produce strange attractors that are significantly more chaotic (larger Lyapunov expon...

A variant of the Hénon map is described in which the linear term is replaced by one that involves a much earlier iterate of the map. By varying the time delay, this map can be used to explore the transition from low-dimensional to high-dimensional dynamics in a chaotic system with minimal algebraic complexity, including a detailed comparison of the Kaplan-Yorke and correlation dimensions. The h...

The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fréchet space. The other is about the chaoticity of a translation map in the space of real continuous functions. The chaos is shown in the senses of both Li-Yorke and Wiggins. Treating dimensions a...

This paper considers a Cournot duopoly model assuming isoelastic demand and smooth cost functions with built-in capacity limits. When the firms cannot obtain positive profits they are assumed to choose small "stand-by" outputs rather than closing down, in order to avoid substantial fitting up costs when market conditions turn out more favorable. It is shown that the model provides chaotic behav...

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...