Offset Boosting-Entangled Complex Dynamics in the Memristive Rulkov Neuron

A discrete memristor is introduced into the Rulkov neuron to mimic biological neuronal synapse and modify firing dynamics. In the memristive Rulkov neuron, chaotic firing with local amplitude control is obtained, where the range of chaotic bursting can be modified by two independent controllers. These two independent bifurcation parameters provide direct amplitude/frequency control. Furthermore, offset boosting-entangled complex dynamics are captured, where the initial condition of the membrane potential can visit any of the self-reproducing attractors and even modify the complex firing, indicating the coexistence of homogeneous and heterogeneous multistabilities. Consequently, a CH32-based circuit is developed to verify various firing activities. The pseudo-random number generator results are explored based on the National Institute of Standards and Technology showing its higher performance in secure optical communication, which is further proved in the seven-core 2-km communication setup.