Lorenz and Rössler Systems with Piecewise-Linear Vector Fields

Classical wavelet systems over finite fields

This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...

On the Existence and Uniqueness of Limit Cycles in Planar Piecewise Linear Systems without Symmetry

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter pro...

Homoclinic orbits in a piecewise linear Rössler-like circuit

In addition to the well-known Rössler funnel that consists in near-homoclinic orbits, perfect homoclinic orbits have been found numerically and experimentally in a simplest piecewise linear Rössler-like electronic circuit. The evolution of the system in the homoclinic range exhibits period-bubbling and period-adding cascades when a control parameter is changed. A scaling law in the period-addin...

On the Kamke-Müller conditions, monotonicity and continuity for bi-modal piecewise-smooth systems

We show that the Kamke-Müller conditions for bimodal piecewise-smooth systems are equivalent to simple conditions on the vector fields defining the system. As a consequence, we show that for a specific class of such systems, monotonicity is equivalent to continuity. Furthermore, we apply our results to derive a stability condition for piecewise positive linear systems.

Piecewise Constant Controlled Linear Fuzzy Systems