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. Attached Files Name Description MIMEType Size Downloads Title Dynamical analysis of the Hindmarsh-Rose neuron with time delays Author(s) Lakshmanan, S orcid.org/0000-0002-4622-3782 Lim, C.P. orcid.org/0000-0003-4191-9083 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 2162-2388 Keyword(s) Time delay Chaos Hopf bifurcation linear matrix inequality (LMI) stability synchronization 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 Persistent URL http://hdl.handle.net/10536/DRO/DU:30087835 Document type: Journal Article Collection: Centre for Intelligent Systems Research Related Links Link Description Connect to Elements publication management system Go to link with your DU access privileges   Connect to published version Go to link with your DU access privileges     Unless expressly stated otherwise, the copyright for items in DRO is owned by the author, with all rights reserved. Versions Version Filter Type Thu, 20 Oct 2016, 12:12:26 EST Thu, 27 Oct 2016, 08:22:42 EST Mon, 16 Jan 2017, 13:58:13 EST Mon, 30 Jan 2017, 07:32:49 EST Thu, 30 Mar 2017, 05:04:54 EST Tue, 06 Jun 2017, 09:29:27 EST Tue, 06 Jun 2017, 09:32:22 EST Tue, 06 Jun 2017, 12:44:03 EST Filtered Full Citation counts:   Cited 0 times in TR Web of Science Cited 0 times in Scopus Search Google Scholar Access Statistics: 21 Abstract Views, 2 File Downloads  -  Detailed Statistics Created: Mon, 16 Jan 2017, 13:58:13 EST

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