Hysteretic Dynamics, Space Magnetization and Offset Boosting in a Third-Order Memristive System

In the present contribution, we investigate the dynamics of a third-order memristive system with only the origin as equilibrium point previously proposed in Kountchou et al. (Int J Bifurc Chaos 26(6):1650093, 2016). Here, the nonlinear component necessary for generating chaotic oscillations is designed using a memristor with fourth-degree polynomial function. Standard nonlinear analysis techniques are exploited to illustrate different chaos generation mechanisms in the system. One of the major results in this work is the finding of some windows in the parameters’ space in which the system experiences hysteretic dynamics; characterized by the coexistence of two and four different stable states for the same set of system parameters. Basins of attraction of various competing attractors are plotted showing complex basin boundaries. The magnetization of state space justifies jump between coexisting attractors. Furthermore, the model exhibits offset-boosting property with respect to a single variable. To the best of the authors’ knowledge, these interesting and striking behaviors (coexisting bifurcations and offset-boosting property) have not yet been reported in a third-order memristive system with only one equilibrium point in view of previously published systems with self-excited attractors. Some Pspice simulations are carried out to validate the theoretical analyses.