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Dynamical analysis of the Hindmarsh-Rose neuron with time delays

Lakshmanan, S, Lim, C.P., Nahavandi, S., Prakash, M and Balasubramaniam, P 2016, Dynamical analysis of the Hindmarsh-Rose neuron with time delays, IEEE transactions on neural networks and learning systems, pp. 1-6, doi: 10.1109/TNNLS.2016.2557845.

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Title Dynamical analysis of the Hindmarsh-Rose neuron with time delays
Author(s) Lakshmanan, SORCID iD for Lakshmanan, S
Lim, C.P.ORCID iD for Lim, C.P.
Nahavandi, S.
Prakash, M
Balasubramaniam, P
Journal name IEEE transactions on neural networks and learning systems
Start page 1
End page 6
Total pages 6
Publisher Institute of Electrical and Electronics Engineers
Place of publication Piscataway, N.J.
Publication date 2016
ISSN 2162-237X
Keyword(s) Time delay
Hopf bifurcation
linear matrix inequality (LMI)
Summary This 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.
Notes In press
Language eng
DOI 10.1109/TNNLS.2016.2557845
Field of Research 099999 Engineering not elsewhere classified
Socio Economic Objective 0 Not Applicable
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2016, IEEE
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Document type: Journal Article
Collection: Centre for Intelligent Systems Research
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