Bifurcation without parameters in circuits with memristors: A DAE approach

Abstract

Bifurcations without parameters describe qualitative changes in the local dynamics of nonlinear ODEs when normal hyperbolicity of a manifold of equilibria fails. Non-isolated equilibrium points are systematically exhibited by nonlinear circuits with memristors; a memristor is a nonlinear device recently introduced in circuit theory and which is expected to play a key role in electronics in the near future. In this communication we provide a graph-theoretic analysis of the transcritical bifurcation without parameters in memristive circuits, owing to the presence of a locally active memristor. The results are crucially based on the use of differential-algebraic circuit models.