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The route to synchrony via drum head mode and mixed oscillatory state in star coupled Hindmarsh–Rose neural network

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  • Usha, K.
  • Subha, P. A.
  • Nayak, Chitra R.

Abstract

Network of coupled oscillators exhibit different types of spatiotemporal patterns. We report that as the coupling strength increases the unidirectionally coupled Hindmarsh–Rose neuron star network will synchronize. The condition for synchronization has been evaluated using Lyapunov function method. We also discuss the dynamics of the system in the presence of controllers. The control input generate interesting behaviors which consist of clusters of spatially coherent domains depending on the coupling strength. Drum head mode, mixed oscillatory state, desynchrony, and multi cluster states are formed and cluster reduction takes place before settling to complete synchrony. The evolution of a perfectly synchronized state via drum head mode, mixed oscillatory state, and clusters from a desynchronized state is reported for the first time. The parameter values which lead to stable cluster formation is also discussed. Our results suggest that in the presence of controllers the common oscillator in the star network behaves as a driver and generates the transitions and cluster formation acts as a precursor to complete synchrony in Hindmarsh–Rose model with unidirectional star coupling.

Suggested Citation

  • Usha, K. & Subha, P. A. & Nayak, Chitra R., 2018. "The route to synchrony via drum head mode and mixed oscillatory state in star coupled Hindmarsh–Rose neural network," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 25-31.
    • Handle: RePEc:eee:chsofr:v:108:y:2018:i:c:p:25-31
    DOI: 10.1016/j.chaos.2018.01.016
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    References listed on IDEAS

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    1. Iryna Omelchenko & Yuri Maistrenko & Erik Mosekilde, 2005. "Synchronization in ensembles of coupled maps with a major element," Discrete Dynamics in Nature and Society, Hindawi, vol. 2005, pages 1-17, January.
    2. Bin, Deng & Jiang, Wang & Xiangyang, Fei, 2006. "Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 182-189.
    3. Kalpathy, Ravi & Ward, Mark Daniel, 2014. "On a leader election algorithm: Truncated geometric case study," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 40-47.
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    Cited by:

    1. An, Xinlei & Qiao, Shuai, 2021. "The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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