The Computation of Two-Dimensional Manifold for Hindmarsh-Rose Neuron Model

Abstract

The Hind marsh-Rose (HR) Neuron not only contained the features of cell biological physical model, but also included the traits of non-linear dynamical system model. The paper analyzed the HR model by computing manifold. It computed the equilibria, simulated the bifurcation phenomenon of the parameters, estimated the unstable local manifold and computed the global manifold using the angle constraint method. The simulation results showed the trend of the unstable manifold and the distribution of the trajectories. It offered good results to study the chaos phenomenon of the HR mode.