On the dynamics of chaotic circuits based on memristive diode-bridge with variable symmetry: A case study

It is widely accepted that for any physical system, symmetries are rarely exact. Therefore, some symmetry imperfections must be always assumed to be present. The dynamics of memristor-based chaotic circuits with symmetric hysteresis loop is well documented. However, only a few works are devoted to the dynamics of these types of circuits when the current-voltage characteristic of the considered memristor is no longer symmetrical. Accordingly, we consider in this work (as a case study) the dynamics of a generalized memristive diode-bridge-based jerk circuit whose symmetry can be varied. We denote by $k$ the dissymmetry coefficient. The tools used for the analysis are the Routh-Hurwitz criterion, bifurcation diagrams, phase portraits, and basins of attraction. It is shown that in the symmetric configuration (i.e. when $k=1.0$) there are three symmetric equilibria whereas in the asymmetric configuration (i.e. when $k\ne 1.0$) we always have two equilibrium with fixed position in state space and a third one whose location varies according to the value of the dissymmetry coefficient. The intrinsic nonlinearity of the memristor is responsible for the plethora of nonlinear and complex behaviours observed in both configurations. These include the coexistence of symmetric and asymmetric attractors, coexisting symmetric and asymmetric bubbles of bifurcation, and symmetric and asymmetric double-scroll chaotic attractors, just to name a few. In addition, the experimental investigations agree well with the results of theoretical and numerical studies.