AC-induced coexisting asymmetric bursters in the improved Hindmarsh-Rose model

In this paper, an external alternating current (AC) is injected into the Hindmarsh-Rose (HR) neuron model to imitate the periodic stimulus effect on the membrane potential in the axon of a neuron and then an improved HR model is proposed. The AC equilibrium point and its stability in the proposed model are investigated theoretically, and the AC-induced coexisting behaviors of asymmetric bursters are revealed by MATLAB numerical simulations. Due to the injection of the AC item, the stability distribution of the unique AC equilibrium point in the improved HR model varies between unstable and stable intervals with the periodic evolution of the time, which leads to the emergence of various types of coexisting asymmetric bursters under different initial conditions of the bursting variable, such as hyperchaotic and periodic bursters, chaotic and periodic bursters, quasiperiodic and periodic bursters, two periodic bursters with different periodicities, and so on. Additionally, a simulated circuit model is designed and PSIM circuit simulations are performed to exhibit coexisting behaviors of asymmetric bursters, which effectively confirm the numerically simulated results.