Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise only for sufficiently strong chaos. In this paper, a Hamiltonian ratchet accelerator is introduced, featuring a momentum current for arbitrarily weak chaos. Th...

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by...

This paper studies basic dynamics from a novel pulse-coupled network (PCN). The unit element of the PCN is an integrate-and-fire circuit (IFC) that exhibits chaos. We an give an iff condition for the chaos generation. Using two IFC, we construct a master-slave PCN. It exhibits interesting chaos synchronous phenomena and their breakdown phenomena. We give basic classification of the phenomena an...

In this letter, chaos in a current-mode controlled boost converter is studied. Firstly, the existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of a one-sided shift map, which implies positive entropy of the system and hence chaotic behavior. The essential tool is the horseshoe hypotheses proposed by K...

In this paper, we solve the two-dimensional advection-diffusion equation with random transport velocity. The generalized polynomial chaos expansion is employed to discretize the equation in random space while the spectral/hp element method is used for spatial discretization. Numerical results which demonstrate the convergence of generalized polynomial chaos are presented. Specifically, it appea...

the problem discussed in this paper is the effect of latency time on the ogy chaos control methodology in multi chaotic systems. the smith predictor, rhythmic and memory strategies are embedded in the ogy chaos control method to encounter loop latency. a comparison study is provided and the advantages of the smith predictor approach are clearly evident from the closed loop responses. the comple...

This paper is concerned with chaos induced by strictly turbulent maps in noncompact sets of complete metric spaces. Two criteria of chaos for such types of maps are established, and then a criterion of chaos, characterized by snap-back repellers in complete metric spaces, is obtained. All the maps presented in this paper are proved to be chaotic either in the sense of both Li–Yorke and Wiggins ...

Modifying the onset of homoclinic chaos. Abstract We analyze, by means of Melnikov method, the possibility of modifying the threshold of homoclinic chaos in general 1-dimensional problems, by introducing small periodic resonant modulations. We indicate in particular a prescription in order to increase the threshold (i.e. to prevent chaos), and consider then its application to the bistable Duffi...

An old problem, but a new area of fundamental research, is characterizing orbital dynamics and its consequences in time-dependent potentials. Regarding nonequilibrium space-charge potentials, one clear consequence is halo formation. We show that orbital chaos normally plays a central role in halo formation. In turn, the ability to quantify chaos is centrally important. We show examples of the g...