By studying laser systems with multiple time delays, we demonstrate that the signatures of time delays in the autocorrelation coefficient and the mutual information of the laser output can be erased for systems with variable time delays. This property makes such laser systems highly suitable for secure chaos-based communication systems. We also present the first report on chaos synchronization ...

A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos...

We report on an experimental observation of optical wave chaos in a resonator consisting of three standard, high-reflectivity mirrors. The nonseparability of the wave equation necessary for chaos is introduced by violating the paraxial approximation. Until recently progress in optical wave chaos was hampered by the inherent difficulty in realizing suitable microscopic systems; now this novel, m...

In this paper, we derive new results for global chaos control of chaotic systems via sliding control. We also explore the analysis and global chaos control of the hyperchaotic Li system (2005) using sliding control. The global chaos control results via sliding control have been established using Lyapunov stability theory. Numerical simulations using MATLAB are shown to validate and depict the e...

Recent work has shown that chaos-based communication systems can yield performances as good as their non-chaotic counterparts in additive white Gaussian noise (AWGN), and behave even better in flat-fading channels. However, much of this work relies on computer simulations and there is still a need to study in depth the implementation issues of such systems. The authors address for the first tim...

The modern concept of deterministic chaos arises from the mathematical and physical investigation of the topological and dynamical properties of deterministic systems. The notion of deterministic chaos is frequently used in an increasing number of scientific as well as non-scientific contexts, ranging from mathematics and the physics of dynamical systems to all sorts of complicated time evoluti...

Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gibbs (BG) statistical mechanics has suggested the potential verification of these generalizations at the onset of chaos, when the only Lyapunov expon...

the origin the concept of lz compexity is in information science. here we use this notion to characterize chaotic dynamical systems. we make contact with the usual characteristics of chaos, such as lyapunov exponent and k-entropy. it is shown that for a two-dimensional system lz complexity is as powerful as other characteristics. we also apply lz complexity to the study of the quasiperiodic fib...

Nearly thirty years of chaos research have shown that chaos is an ubiquitous phenomenon. Almost any dynamical system with a sufficiently large phase space described by nonlinear equations shows some kind of complexity in its time evolution, i.e. chaos. The degree of complexity is measured by topological entropy, Lyapunov exponents, decay of correlations, and, in the case of dissipative systems,...

A mapping method for distributive mixing with diffusion: Interplay between chaos and diffusion in time-periodic sine flow Conor P. Schlick,1,a) Ivan C. Christov,1,2,b) Paul B. Umbanhowar,3 Julio M. Ottino,2,3,4 and Richard M. Lueptow3,4,c) 1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA 2Department of Chemical and Biological En...