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Dynamical analysis of the Hindmarsh-Rose neuron with time delays
journal contribution
posted on 2017-08-01, 00:00 authored by S Lakshmanan, Chee Peng LimChee Peng Lim, Saeid Nahavandi, M Prakash, P BalasubramaniamThis brief is mainly concerned with a series of dynamical analyses of the Hindmarsh-Rose (HR) neuron with state-dependent time delays. The dynamical analyses focus on stability, Hopf bifurcation, as well as chaos and chaos control. Through the stability and bifurcation analysis, we determine that increasing the external current causes the excitable HR neuron to exhibit periodic or chaotic bursting/spiking behaviors and emit subcritical Hopf bifurcation. Furthermore, by choosing a fixed external current and varying the time delay, the stability of the HR neuron is affected. We analyze the chaotic behaviors of the HR neuron under a fixed external current through time series, bifurcation diagram, Lyapunov exponents, and Lyapunov dimension. We also analyze the synchronization of the chaotic time-delayed HR neuron through nonlinear control. Based on an appropriate Lyapunov-Krasovskii functional with triple integral terms, a nonlinear feedback control scheme is designed to achieve synchronization between the uncontrolled and controlled models. The proposed synchronization criteria are derived in terms of linear matrix inequalities to achieve the global asymptotical stability of the considered error model under the designed control scheme. Finally, numerical simulations pertaining to stability, Hopf bifurcation, periodic, chaotic, and synchronized models are provided to demonstrate the effectiveness of the derived theoretical results.
History
Journal
IEEE transactions on neural networks and learning systemsVolume
28Issue
8Pagination
1953 - 1958Publisher
Institute of Electrical and Electronics EngineersLocation
Piscataway, N.J.Publisher DOI
ISSN
2162-237XeISSN
2162-2388Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2016, IEEEUsage metrics
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No categories selectedKeywords
Time delayChaosHopf bifurcationlinear matrix inequality (LMI)stabilitysynchronizationScience & TechnologyTechnologyComputer Science, Artificial IntelligenceComputer Science, Hardware & ArchitectureComputer Science, Theory & MethodsEngineering, Electrical & ElectronicComputer ScienceEngineeringlinear matrixinequality (LMI)BIFURCATION-ANALYSISFEEDBACKMODELS
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