Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model

Abstract

Mathematics has changed over time to comprise interdisciplinary fields of research, and consid- ering this, biomathematics has arisen as an interface study. In this work, we analyze the dynamical behavior of the Hindmarsh-Rose neuron model, which describes the neuronal bursting in a single neuron. A stability study through the Lyapunov exponents method is proposed and evidence of a chaotic dynamics is presented. This chaotic behavior is biologically comparable to an individual undergoing an epileptic seizure, in which the application of an efficient controller represents a proposal for preventing epilepsy from happening. Therefore, a control design based on the State-Dependent Riccati Equation 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.