Energy-based initials-boosted firings in memristor synapse-coupled bi-mRulkov neuron network

The energy interaction-induced firing and synchronization activities in existing neuronal networks have recently garnered attention. However, the initials-boosted extreme multistability and synchronization firings supplied by the field energy simulated with memristors have not been extensively documented. Therefore, it is of paramount importance to integrate Hamilton energy and dynamics in exploring these novel behaviors to unveil the physical essence of neuronal firing, enhance network flexibility and controllability, and reinforce the practical value of networks. To address these issues, using a memristor synapse to connect two Rulkov neurons that are exposed to memristive electromagnetic radiation, we construct a bionic memristor synapse-coupled bi-mRulkov neuron network model, known as the bi-mRulkov network. It possesses spatial equilibrium points, topological invariance, and synchronization convergence associated with the initial conditions of memristors. In particular, by establishing quantitative indicators based on the Hamilton energy and synchronization factor, the interesting boosting firing and its energy balance and transition processes are visualized from the two-dimensional plane and local dynamics. Theoretical analysis and numerical simulation demonstrate that the bi-mRulkov network can generate the boosting extreme multistability firing. Furthermore, the complex line-boosted complete synchronization and plane-boosted parallel offset synchronization firings are determined by the memristor-controlled energy balance and transition, respectively. Finally, both the PSpice-based analog circuit and microcontroller-based digital circuit platforms are developed to validate the abundant firing activities, which offers accurate implementation paradigms for the proposed neuronal network.