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...

We propose a new method to investigate collective behavior in a network of globally coupled chaotic elements generated by a tent map. In the limit of large system size, the dynamics is described with the nonlinear FrobeniusPerron equation. This equation can be transformed into a simple form by making use of the piecewise linear nature of the individual map. Our method is applied successfully to...

In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley–Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous ver...

We introduce in this paper a new chaotic map with dynamical properties controlled by two free parameters. The map definition is based on the hyperbolic tangent function, so it is called the tanh map. We demonstrate that the Lyapunov exponent of the tanh map is robust, remaining practically unaltered with the variation of its parameters. As the main application, we consider a chaotic communicati...

In this paper a theoretical approach for studying the effects of parameter perturbations on the chaotic statistics of piecewise linear expanding transformations is summarized, with reference to the chaotic Sawtooth map. On this basis, the authors prove that is possible, both from a theoretical and from an experimental point of view, to obtain almost uniform distributed and uncorrelated analog s...

In the present paper, we introduce and analyze a mechanical system, in which the digital implementation of a linear control loop may lead to chaotic behavior. The amplitude of such oscillations is usually very small, this is why these are called micro-chaotic vibrations. As a consequence of the digital effects, i.e. the sampling, the processing delay and the round-off error, the behavior of the...

This paper studies nonlinear dynamics of a simplified model of multiple-input parallel buck converters. The dynamic winnertake-all switching is used to achieve N-phase synchronization automatically, however, as parameters vary, the synchronization bifurcates to a variety of periodic/chaotic phenomena. In order to analyze system dynamics we adopt a simple piecewise constant modeling, extract ess...

chaos-based encryption methods have been presented and discussed in the last two decades. In order to reach higher performance, these methods take advantage of the more and more complex behavior of chaotic signals. This paper contributes in this issue by comparing the performance of the well known piecewise linear chaotic map (PWLCM) with that of PWLCM perturbed by a new technique. Both chaotic...