Repetitive Firing and Bursting due to Different Bifurcation Mechanism in Unmyelinated Fibre

In neural science, different action potential (AP) firing patterns are typically considered to be dominated by different dynamical mechanisms. Different AP firing patterns in unmyelinated fibres can contribute to pain and sensory information transmission. Experiments in rabbit unmyelinated nerve (axon) show some interesting phenomena, mainly concerned with the AP firing patterns that changed regularly. Investigating the dynamical mechanism of unmyelinated fibre during various kinds of AP firing patterns is useful to understand the neural information processing in axon and pain information transmission. Here, we reproduced these phenomena by constructing a mathematical model, where the discharge of the Hodgkin-Huxley (H-H) neuron under square wave stimulation was studied by simulation. It is shown that square wave can induce bursting firing, especially with long time-course duration. This is different from the popular theory that explained repetitive and bursting firing due to stimulus intensity and instantaneous fluctuation. Through dynamical analysis, we found that the mechanism of the action potential pattern changed according to Hopf bifurcation, a dynamical behavior that emergence and stability of limit cycles of bifurcating from a stable equilibrium. The finding may support the neural information coding hypothesis in unmyelinated axon.