Generation of chaotic attractors without equilibria via piecewise linear systems

In this paper, we present a mechanism of generation of a class of switched dynamical system without equilibrium points that generates a chaotic attractor. The switched dynamical systems are based on piecewise linear (PWL) systems. The theoretical results are formally given through a theorem and corollary which give necessary and sufficient conditions to guarantee that a linear affine dynamical system has no equilibria. Numerical results are in accordance with the theory.

BIFURCATION ANALYSIS IN A PWM CURRENT-CONTROLLED H-BRIDGE INVERTER

This paper introduces the complete bifurcation analysis in a PWM current-controlled H-Bridge inverter in a wide parameter space. First, we briefly explain the behavior of the waveform in the circuit in terms of the switched dynamical system. Then, the consecutive waveform during the duration of the clock interval is exactly discretized, and the return map is defined for the rigorous analysis. Using the map, we derive the one- and two-dimensional bifurcation diagrams, and discuss the specific property of each bifurcation phenomena in the circuit.

Chaotic Behavior in a Switched Dynamical System

We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator) which is a Scilab (scientific laboratory) package. The followed approach takes into account the hybrid nature of the circuit.