Dynamics analysis and DSP implementation of the Rulkov neuron model with memristive synaptic crosstalk

Abstract The human brain is a complex intelligent system composed of tens of billions of neurons interconnected through synapses, and its intricate network structure has consistently attracted numerous scientists to explore the mysteries of brain functions. However, most existing studies have only verified the biological mimicry characteristics of memristors at the single neuron-synapse level, and there is still a lack of research on memristors simulating synaptic coupling between neurons in multi-neuron networks. Based on this, this paper uses discrete memristors to couple dual discrete Rulkov neurons, and adds synaptic crosstalk between the two discrete memristors to form a neuronal network. A memristor-coupled dual-neuron map, called the Rulkov–memristor–Rulkov (R-M-R) map, is constructed to simulate synaptic connections between neurons in biological tissues. Then, the equilibrium points of the R-M-R map are studied. Subsequently, the effect of parameter variations on the dynamic performance of the R-M-R map is comprehensively analyzed using bifurcation diagram, phase diagram, Lyapunov exponent spectrum (LEs), firing diagram, and spectral entropy (SE) complexity algorithms. In the R-M-R map, diverse categories of periodic, chaotic, and hyperchaotic attractors, as well as different states of firing patterns, can be observed. Additionally, different types of state transitions and coexisting attractors are discovered. Finally, the feasibility of the model in digital circuits is verified using a DSP hardware platform. In this study, the coupling principle of biological neurons is simulated, the chaotic dynamic behavior of the R-M-R map is analyzed, and a foundation is laid for deciphering the complex working mechanisms of the brain.