Analysis of Chaos Route in Hybridized FitzHugh-Nagumo Neuron Model

Recently, several hybrid spiking neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process to avert divergence after spiking, have been proposed. Izhikevich neuron model as this kind of model is known to be able to reproduce diverse spiking patterns including chaotic spiking. To reveal the factor for this high diversity, it is necessary to evaluate the influence of the state dependent jump on the trajectory in a continuous system through the comparison between the system with/without the resetting process. However, if the resetting process is removed, the orbit in Izhikevich neuron model exhibits only the divergent behavior at a spiking state. This means that Izhikevich neuron model can not be used to evaluate the changes of attractor’s structure by adding the resetting process. In this paper, we introduced the resetting process to the conventional FitzHugh-Nagumo neuron model where the orbit at a spiking state does not diverge. And then we compared the bifurcation and the structure of attractors between this hybridized FitzHugh-Nagumo neuron model with this resetting process and the conventional one. As the result, it was confirmed that non-linear stretching and folding structure of the attractor is induced by the resetting process and the chaotic state emerges through a tangent bifurcation depending on the distance of jump.