Homoclinic orbits in a piecewise linear Rössler-like circuit

Abstract

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-adding cascade between the period of a homoclinic orbit and the bifurcation parameter is evaluated. Other phenomena, such as the coexistence of two homoclinic orbits, homoclinic chaos, symmetry breaking and phase bistability are also demonstrated. The results of numerical simulations are in a good agreement with experiments. © 2005 IOP Publishing Ltd.