DC-bias induced chaotic dynamics and periodic bursting in Chua's diode-based FitzHugh-Nagumo circuit

Bursting is a dynamic state in which a neuron repeatedly fires isolated groups or bursts of spikes. Neuronal bursting can play a crucial role in communication between neurons. To construct a simple neural circuit within the FitzHugh-Nagumo (FHN) circuit framework, this paper develops a second-order Chua's diode-based FHN (CD-FHN) circuit with DC-bias voltage. It is characterized by a two-dimensional non-autonomous piecewise-linear system. With this piecewise-linear system, the DC-bias related invariant point with stability evolution is discussed, and the DC-bias induced chaotic dynamics is revealed when the CD-FHN circuit uses a large-amplitude and high-frequency AC voltage source. Taking the DC-bias voltage as a variable parameter and using a small-amplitude and low-frequency AC voltage source in the CD-FHN circuit, the dynamical behaviors with period-adding bifurcation are explored, and the DC-bias induced quasi-periodic spiking and periodic bursting modes are disclosed. The results show that the orbit of the periodic bursting mode can be switched between the spiking and quiescent states via the boundary equilibrium bifurcation with bifurcation delay. Finally, both circuit simulations and analog experiments are executed to well verify the numerical results, demonstrating that the CD-FHN circuit can be induced by DC-bias voltage to present chaotic dynamics, quasi-periodic spiking, and periodic bursting.