Dynamics and synchronization of fractional-order Rulkov neuron coupled with discrete fracmemristor

Memristors play an important role in the modeling of neural networks as external stimuli for neuron excitation and biological synapses for information exchange. Recently, the discrete fracmemristor has shown excellent properties in describing the memory effect of nonlinear systems, including biological nervous systems. In this paper, we propose a fractional memristive Rulkov neuron model (FMRN) by introducing the fractional discrete HP-type memristor (FDM-HP) into a single fractional Rulkov neuron (FRN) as electromagnetic radiation. Their parametric modulation dynamics are investigated and compared by means of firing patterns, Lyapunov exponents, bifurcation diagrams and complexity. In addition, to verify the information transfer ability of discrete fracmemristor as a synaptic model, a fractional bi-neuron system is constructed by coupling two FRNs with FDM-HP, which is further subjected to the analyses of phase synchronization and firing behaviors. The simulation results show that the combination of FDM-HP and FRN can effectively enrich the dynamics of neuron system, achieve synchronous firing rhythms, and generate various novel firing patterns. The researches provide the theoretical and experimental supports for neuronal modeling and synapse-based synchronization, which lay the foundation for further researches on complex neural networks.