Nonlinear Dynamics, Switching Kinetics and Physical Realization of the Family of Chua Corsage Memristors

Action potential and chaos near the edge of chaos in memristive circuits

Memristor-based neuromorphic systems have a neuro-bionic function, which is critical for possibly overcoming Moore's law limitation and the von Neumann bottleneck problem. To explore neural behaviors and complexity mechanisms in memristive circuits, this paper proposes an N-type locally active memristor, based on which a third-order memristive circuit is constructed. Theoretical analysis shows that the memristive circuit can exhibit not only various action potentials but also self-sustained oscillation and chaos. Based on Chua's theory of local activity, this paper finds that the neural behaviors and chaos emerge near the edge of chaos through subcritical Hopf bifurcation, in which the small unstable limit cycle is depicted by the dividing line between the attraction basin of the large stable limit cycle and the attraction basin of the stable equilibrium point. Furthermore, an analog circuit is designed to imitate the action potentials and chaos, and the simulation results are in agreement with the theoretical analysis.

Generation of Multi-Lobe Chua Corsage Memristor and Its Neural Oscillation

The Chua corsage memristor (CCM) is considered as one of the candidates for the realization of biological neuron models due to its rich neuromorphic behaviors. In this paper, a universal model for m-lobe CCM memristor is proposed. Moreover, a novel small-signal equivalent circuit with one capacitor is derived based on the proposed model to determine the edge of chaos and obtain the zero-pole diagrams and analyze the frequency response and oscillation mechanism of the m-lobe CCM system, which are discussed in detail. In view of existence of the edge of chaos, the frequency response and the oscillation mechanism of the simplest oscillator is analysed using the proposed model. Finally, the proposed model has exhibited some essential neural oscillation, including the stable limit cycle, supercritical Hopf bifurcation, spiking and bursting oscillation. This study also reveals a previously undiscovered behavior of bursting oscillation in a CCM system.

Locally active memristor based oscillators: The dynamic route from period to chaos and hyperchaos

To explore the complexity of the locally active memristor and its application circuits, a tristable locally active memristor is proposed and applied in periodic, chaotic, and hyperchaotic circuits. The quantitative numerical analysis illustrated the steady-state switching mechanism of the memristor using the power-off plot and dynamic route map. For any pulse amplitude that can achieve a successful switching, there must be a minimum pulse width that enables the state variable to move beyond the attractive region of the equilibrium point. As local activity is the origin of complexity, the locally active memristor can oscillate periodically around a locally active operating point when connected in series with a linear inductor. A chaotic oscillation evolves from periodic oscillation by adding a capacitor in the periodic oscillation circuit, and a hyperchaotic oscillation occurs by further putting an extra inductor into the chaotic circuit. Finally, the dynamic behaviors and complexity mechanism are analyzed by utilizing coexisting attractors, dynamic route map, bifurcation diagram, Lyapunov exponent spectrum, and the basin of attraction.