Chaotic bursting and burst synchronization in a discrete dual-Rulkov neural network with memristive synaptic coupling

Abstract A discrete dual-Rulkov neural network with memristive synaptic coupling is constructed to investigate chaotic bursting dynamics and burst synchronization. First, a memristive synapse model suitable for discrete-time neurons is established, and its pinched hysteresis loop (PHL) fingerprint and local activity are verified. Based on this synapse model, a five-dimensional memristively coupled discrete neural system is formulated. By combining Lyapunov exponent spectra (LEs), bifurcation analysis, and equilibrium stability analysis, chaotic and hyperchaotic bursting behaviors induced by variations in the coupling gain are revealed, together with their dynamical evolution characteristics. Furthermore, to characterize irregular spiking activities during chaotic bursting, a joint framework based on the phase-locking value (PLV) and burst envelope correlation (EnvCorr) is introduced, through which three bursting regimes, namely, in-phase bursting (IPB), phase-shifted bursting (PSB), and desynchronized bursting (DB), are identified. Finally, a digital signal processor (DSP)-based real-time hardware implementation is carried out, and the good qualitative agreement between experimental and numerical results demonstrates the physical feasibility of the proposed model.