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.

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...

We study the discrete dynamics of interval maps generated by action erasing block substitutions on binary expansion. propose a classification in hierarchy classes displaying progressively stronger character. investigate how this affects corresponding maps, showing that richest dynamical behavior (Devaney and Li-Yorke chaos, infinite topological entropy) is achieved at precise step hierarchy, wh...

The paper contains a rigorous proof of existence symbolic dynamics chaos in the generalized H\'enon map's 4th iterate $H^4$, which was conjectured \textit{A 3D Smale Horseshoe Hyperchaotic Discrete-Time System} Li and Yang, 2007. We prove also uniform hyperbolicity invariant set with dynamics. proofs are computer-assisted use C++ library \textit{CAPD} for interval arithmetic, differentiation in...

This paper presents a new hyperchaotic system with three positive Lyapunov exponents (called Tri-Chaos). Via linear coupling, Mathieu, and van der Pol systems are coupled with each other and then become a new four order system—Mathieu–van der Pol autonomous system. As we know, two positive Lyapunov exponents confirm hyperchaotic nature of its dynamics and it means that the system can present mo...

The paper analyzes the dynamic properties of the neoclassical one-sector growth model with di!erential savings in the sense of Kaldor}Pasinetti. The economy exhibits unstable steady states and #uctuations if the income distribution varies su$ciently and if shareholders save more than workers. The paper analyzes in detail the dynamics for the case with a "xed proportions technology as well as wi...

This paper is devoted to an in-depth study of cellular automaton rule 180 under the framework of symbolic dynamics. Rule 180, a member of Wolfram’s class IV and Chua’s hyper Bernoulli shift rules, defines infinite number of generalized sub-shifts. An effective method of constructing the shift invariant sets of the rule’s global map is proposed. It is noted that this method is also applicable to...

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...