Chaos and bursting patterns in two-neuron Hopfield neural network and analog implementation

Fangyuan Li, Zhuguan Chen, Han Bao, Lianfa Bai and Bocheng Bao

Chaos, Solitons & Fractals, 2024, vol. 184, issue C

Abstract: To demonstrate and elucidate bursting patterns and their bifurcation mechanisms, a two-neuron Hopfield neural network is proposed in this paper. The proposed non-autonomous model has a time-varying equilibrium point whose stability undergoes continuous evolution in response to changes in stimulation, and exhibits chaotic dynamics, especially the quasi-periodic and periodic bursting patterns. Over a full bursting cycle, the stability evolution of the time-varying equilibrium point triggers Hopf bifurcation and fold bifurcation, leading to the emergence of quasi-periodic or periodic bursting. To elucidate the bifurcation mechanisms, the transitions between the spiking state and the resting state are demonstrated, thereby identifying the Hopf/Hopf quasi-periodic bursting and fold/fold/Hopf periodic bursting. In addition, a simple analog electronic circuit is designed for the physical implementation of the non-autonomous model, and a printed-circuit board based hardware circuit is made to test the experimental results to verify the numerical results.

Keywords: Hopfield neural network; Stimulation; Bifurcation; Equilibrium point; Quasi-periodic bursting; Periodic bursting (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005988

DOI: 10.1016/j.chaos.2024.115046

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