Bifurcation Analysis of the Nagumo–Sato Model and Its Coupled Systems

The Nagumo-Sato model is a simple mathematical expression of a single neuron, and it is categorized as a discrete-time hybrid dynamical system. To compute bifurcation sets in such a discrete-time hybrid dynamical system accurately, conditions for periodic solutions and bifurcations are formulated herewith as a boundary value problem, and Newton's method is implemented to solve that problem. As the results of the analysis, the following properties are obtained: border-collision bifurcations play a dominant role in dynamical behavior of the model; chaotic regions are distinguished by tangent bifurcations; and multi-stable attractors are observed in its coupled system. We demonstrate several bifurcation diagrams and corresponding topological properties of periodic solutions.

Electronic version of an article published as International Journal of Bifurcation and Chaos Vol. 26, No. 3, 2015, 1630006, DOI: 10.1142/S0218127416300068 © World Scientific Publishing Company, https://www.worldscientific.com/worldscinet/ijbc