Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
| Autor: | Raildo Santos de Lima, Fabio Chavarette |
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| Přispěvatelé: | Universidade Federal de Mato Grosso do Sul (UFMS), Universidade Estadual Paulista (UNESP) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Scopus Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP |
| Popis: | Made available in DSpace on 2022-05-01T13:41:28Z (GMT). No. of bitstreams: 0 Previous issue date: 2022-01-01 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. Department of Mathematics UFMS - Universidade Federal de Mato Grosso do Sul Department of Mathematics UNESP - Universidade Estadual Pauslita Julio de Mesquita Filho Department of Mathematics UNESP - Universidade Estadual Pauslita Julio de Mesquita Filho |
| Databáze: | OpenAIRE |
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