Analytical Conditions for the Existence of a Homoclinic Loop in Chua Circuits

We analyze a third-order piecewise-linear system that describes the operation of an electronicoscillator. This system can be used to investigate various scenarios for the onset of chaos, in particular, through separatrix loop destruction. Necessary and sufficient conditions are obtained for the existence of an equilibrium separatrix loop. Calculation of critical parameters is illustrated.