Dynamic analysis of coupled Hindmarsh-Rose neurons with enhanced FPGA implementation

Abstract

As the fundamental unit of the nervous system, neuron is essential for transmitting and processing information, playing a critical role in brain activity regulation. This article develops an electrically coupled Hindmarsh-Rose (HR) neurons incorporating external stimuli to simulate biological neuronal behavior. The bifurcation plot with varying the coupling strength of the system are analyzed through the discrete mapping method, in which period-doubling bifurcations and saddle bifurcation are obtained. The evolutions of period-1 to period-8 and period-3 to period-6 are predicted with stable and unstable periodic orbits, and multiple firing behaviors of such a neuron network are studied using Lyapunov exponent and timing-phase diagram. The real part and magnitudes of eigenvalues with varying the coupling strength for different periodic motions are also plotted to illustrate the bifurcation mechanism of the coupled HR neurons. Moreover, theoretical analysis is validated through FPGA technology, which also accelerates computation and minimizes data storage requirements. Ultimately, a uniform linear segmentation algorithm is utilized to construct bifurcation plots of the coupled HR neuron, and experimental results confirm the model's accuracy.