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Generalized synchronization of regulate seizures dynamics in partial epilepsy with fractional-order derivatives

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  • Tene, Alain Giresse
  • Tchoffo, Martin
  • Tabi, Bertrand Conrad
  • Kofane, Timoleon Crepin

Abstract

The dynamical behavior and the synchronization of epileptic seizure dynamics, with fractional-order derivatives, is studied in this paper. Knowing that the dynamical properties of ictal electroencephalogram signal recordings during experiments displays complex nonlinear behaviors, we analyze the system from chaos theory point of view. Based on stability analysis, the system presents three equilibrium points with two of them unstable. Moreover, the system reveals attractor points from the phase portrait analysis. In addition, the largest Lyapunov exponent displays positive values after a given period of time. These observations characterize a chaotic behavior of epileptic seizure dynamics. Therefore, based on the Ge-Yao-Chen partial region stability theory, the synchronization of the system is achieved and simulations prove that the control technique is very efficient. Further studies based on phase synchronization show that we are able to force infected population of neurons by epilepsy into synchronization with uninfected one through a coupling constant. In addition, based on the phase locking value time evolution (phase synchronization) of the system, we realize that fractional-order derivative induces quick synchronization compared to integer order derivative. These results might be very interesting from the medical point of view, because by applying the proposed control method, one may be able to regulate (or reduce) seizure amplitude which, if kindly implemented in practice, will provide excellent therapeutic solution to drug resistant patients with epilepsy.

Suggested Citation

  • Tene, Alain Giresse & Tchoffo, Martin & Tabi, Bertrand Conrad & Kofane, Timoleon Crepin, 2020. "Generalized synchronization of regulate seizures dynamics in partial epilepsy with fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305107
    DOI: 10.1016/j.chaos.2019.109553
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    References listed on IDEAS

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    1. Romanic Kengne & Robert Tchitnga & Alain Kammogne Soup Tewa & Grzegorz Litak & Anaclet Fomethe & Chunlai Li, 2018. "Fractional-order two-component oscillator: stability and network synchronization using a reduced number of control signals," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(12), pages 1-19, December.
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    Cited by:

    1. Borah, Manashita & Das, Debanita & Gayan, Antara & Fenton, Flavio & Cherry, Elizabeth, 2021. "Control and anticontrol of chaos in fractional-order models of Diabetes, HIV, Dengue, Migraine, Parkinson's and Ebola virus diseases," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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