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 multistable attractors are observed in its coupled system. We demonstrate several bifurcation diagrams and corresponding topological properties of periodic solutions.
['Daisuke Ito', 'Tetsushi Ueta', 'Takuji Kousaka', 'Kazuyuki Aihara']
Bifurcation Analysis of the Nagumo–Sato Model and Its Coupled Systems