Neural networks are a relatively new development in computer science, having survived a brush with the exclusive-or problem while the field was still in its teens in the 1960s and recovered for a renaissance in the 1980s. Chaos is a new mathematical theory, dating back to perhaps the 1960s at the earliest and blooming only in the 1980s. The intersection of chaos with neurobiology dates back per...

This paper investigates the adaptive chaos control and synchronization of the Shaw chaotic system (Shaw, 1981) with unknown parameters. First, we design adaptive control laws to stabilize the Shaw chaotic system with unknown parameters to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Next, we derive adaptive control laws to achieve gl...

The theory of chaos and shadowing developed recently by the author is amplified to the case of a heteroclinically tubular cycle. Specifically, let F be a C3 diffeomorphism on a Banach space. F has a heteroclinically tubular cycle that connects two normally hyperbolic invariant manifolds. Around the heteroclinically tubular cycle, a Bernoulli shift dynamics of submanifolds is established through...

We address the problem of quantum chaos: Is there a rigorous, physically meaningful definition of chaos in quantum physics? Can the tools of classical chaos theory, like Lyapunov exponents, Poincaré sections etc. be carried over to quantum systems? Can quantitative predictions be made? We show that the recently proposed quantum action is well suited to answer those questions. As an example we s...

We discuss the creation of hyperchaotic attractors in a system of two coupled Chua circuits. Both mutual and unidirectional couplings are considered. Results from chaos synchronization theory allow us to determine chaos-hyperchaos intermittency.

This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for thes...

The emergence of second-harmonic generation (SHG) is a pivotal issue to the development of nano-optical devices and interfaces. Here, we perform a classical analysis of the SHG dynamics with the aim of determining critical values of the electric field. The signals of the SHG process are nonlinear, so it seems reasonable that chaos theory can be a suitable tool to analyze their dynamics. For thi...

ToToday’s market place is increasingly dynamic and volatile. In this area supply network issues recently have attracted a lot of attention from industrial practitioners and academics worldwide. Chaos theory is the study of complex, nonlinear, dynamic systems. For chaotic systems, a tiny change in conditions may result in an enormous change in system output, whereas substantial changes in condit...

This course offers an overview of the role of information, flows, topology, and synchronization in complex networks. In the first part of the course the students will learn the theory behind these concepts in general terms. In particular, it will be introduced concepts from Ergodic theory, Dynamical Systems, Complex Networks, Theory of information, Networks Flow Theory, and Synchronization Theo...

s of Invited Lectures final: June 18, 2002 http://www.camtp.uni-mb.si/chaos/2002/ On the Weibull distribution appeared in chaotic systems