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

doi:10.1088/1674-1056/ae5f06

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.

Keywords: memristor Rulkov neuron chaotic bursting burst synchronization DSP implementation

Received: 14 March 2026
Revised: 07 April 2026
Accepted manuscript online: 14 April 2026

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Xt	(Synchronization; coupled oscillators)
	87.19.lj	(Neuronal network dynamics)
	87.19.lg	(Synapses: chemical and electrical (gap junctions))

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 62541206, 62502250, and 62571079), the Liaoning Provincial Science and Technology Plan Joint Project (Grant No. 2024-MSLH-033), the Liaoning Provincial Department of Education Basic Scientific Research Projects for Higher Education Institutions (Grant Nos. LJ142510152002 and LJ142510152003), and the Dalian Science and Technology Talent Innovation Support Policy Implementation Plan–Young Science and Technology Star (Grant No. 2025RQ32).

Corresponding Authors: Yinghong Cao
E-mail: caoyinghong@dlpu.edu.cn

Cite this article:

Ke Meng(孟珂), Yifan Bu(卜一帆), Yinghong Cao(曹颖鸿), Suo Gao(高锁), Qi Li(李琦), Chunpeng Wang(王春鹏), and Jun Mou(牟俊) Chaotic bursting and burst synchronization in a discrete dual-Rulkov neural network with memristive synaptic coupling 2026 Chin. Phys. B 35 060501

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

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