This paper surveys some recent results about chaos induced by snap-back repellers and its applications to anti-control of chaos (or, chaotification). Several criteria of chaos induced by snap-back repellers in finite and infinite dimensional dynamical systems are introduced. Some successful applications are given to chaotification problems for finite and infinitedimensional discrete dynamical s...

Nowadays, chaos theory, turbulence and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence (chaos and turbulence engineering), 2. rough dependence on initial data – short term unpredictability (turbulence physics), 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of p...

Abstract Nonuniform slot air bearing (NSAB) systems have two major advantages, the external supply and restrictor design, their inherent multidirectional supporting forces stiffness that provide excellent rotational stability. However, NSAB are prone to vibration from nonperiodic or chaotic motion caused by nonlinear pressure distribution within gas film, imbalance, simply inappropriate design....

Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic, coarse-grained analysis is performed. Relevance of this phenomenon to the problem of quantum chaos is discussed.

This chapter presents an application of neural networks to chaos synchronization. The two main methodologies, on which the approach is based, are recurrent neural networks and inverse optimal control for nonlinear systems. On the basis of the last technique, chaos is first produced by a stable recurrent neural network; an adaptive recurrent neural controller is then developed for chaos synchron...

A large number of analog chaos-based secure communication systems have been proposed since the early 1990s exploiting the technique of chaos synchronization. A brief survey of these chaos-based cryptosystems and of related cryptanalytic results is given. Some recently proposed countermeasures against known attacks are also introduced.

This paper illustrates the presence of chaos in rank-one chaotic systems with delay via a binary test called 0-1 test for chaos. Chaotic synchronization between two rank-one chaotic systems without and with delay is achieved by means of Lyapunov functional and linear delayed feedback control method. Numerical simulations are implemented to verify the effectiveness of the proposed chaos synchron...