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...

This paper introduces Chaos Theory as a means of studying information systems. It argues that Chaos Theory, combined with new techniques for discovering patterns in complex quantitative and qualitative evidence offers a potentially more substantive approach to understand the nature of information systems in a variety of contexts. The paper introduces Chaos Theory concepts by way of an illustrat...

In this paper we prove the occurence of chaos for charged particles moving around a Schwarzschild black hole, perturbed by special classes of electromagnetic fields. The appearance of chaos is studied resorting to the Poincaré-Melnikov method. Submitted to: Class. Quantum Grav. PACS numbers: 04.20.-q, 05.45.-a, 95.10.Fh, 95.30.Sf Chaos in Black Holes Surrounded by Electromagnetic Fields 2

The lectures are centered around three selected topics of quantum chaos: the Selberg trace formula, the two-point spectral correlation functions of Riemann zeta function zeros, and of the Laplace–Beltrami operator for the modular group. The lectures cover a wide range of quantum chaos applications and can serve as a non-formal introduction to mathematical methods of quantum chaos.