Nonlinear dynamics, chaos and control of the Hindmarsh-Rose neuron model

Abstract

Mathematics has changed over time to comprise interdisciplinary fields of research, and considering this, biomathematics has arisen as an interface study. In this work, we analyze the dynamical behavior of the Hindmarsh-Rose (HR) neuron model, which describes the neuronal bursting in a single neuron. A stability study through the Lyapynov exponents method is proposed and evidence of a chaotic dynamics is presented. Therefore, a control design based on the State-Dependent Ricatti Equation (SDRE) is proposed aiming to reduce the oscillation of the system to a desired orbit. The results show that the controller is efficient and robust as a method for preventing epileptic seizures.