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

Fábio Roberto Chavarette; Raildo Santos de Lima

doi:10.5269/bspm.47770

Fábio Roberto Chavarette Universidade Estadual Pauslita “Julio de Mesquita Filho” - UNESP http://orcid.org/0000-0002-1203-7586
Raildo Santos de Lima Universidade Federal de Mato Grosso do Sul - UFMS http://orcid.org/0000-0002-5549-6205

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.

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Author Biographies

Fábio Roberto Chavarette, Universidade Estadual Pauslita “Julio de Mesquita Filho” - UNESP

Department of Mathematics,
UNESP - Universidade Estadual Pauslita “Julio de Mesquita Filho”,
Brasil.

Raildo Santos de Lima, Universidade Federal de Mato Grosso do Sul - UFMS

Department of Mathematics,
UFMS - Universidade Federal de Mato Grosso do Sul,
Brasil.

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