Memristive Single-Neuron Model and Its Memristor-Coupled Network: Homogenously Coexisting Attractors and Parallel-Offset Synchronization

To exhibit chaotic dynamics in a single neuron, a memristive single-neuron model is first constructed by replacing resistive self-synapse weight with memristive self-synapse weight. Stability analysis is performed for its switchable equilibrium point and dynamical behaviors related to the control parameters and initial conditions are explored using numerical simulations. The results show that the memristive single-neuron model can exhibit complex dynamics, especially the homogeneously coexisting chaotic/periodic attractors. Furthermore, to study the dynamical effect of memristor on network synchronization, a memristor-coupled network is constructed by coupling two identical single-neuron models with a memristor. The dynamics induced by the coupling memristor is investigated numerically and synchronous behaviors with different parallel offsets are discovered. The results indicate that the memristor-coupled network can achieve complete synchronization at large coupling strength, and parallel-offset synchronization appears when the memristor initial conditions of two subsystems are mismatched. Finally, a digital microcontroller-based hardware platform is built to verify the correctness of the numerical simulations.