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...

We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-D MPCs exhibit limit-cycle, line-expanding chaos and areaexpanding chaos, respectively. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map which can be expressed explicitly. In order to analyze the p...

This paper studies a small neural network with three neurons. First, the activation function takes the sign function. Although the network is a simple hybrid systemwith all subsystems being exponentially stable, we find that it can exhibit very complex dynamics such as limit cycles and chaos. Since the sign function is a limit case of sigmoidal functions, we find that chaos robustly exists with...

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion ...