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Bursting in a System of Two Coupled Pulsed Neurons with Delay

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Advances in Neural Computation, Machine Learning, and Cognitive Research II (NEUROINFORMATICS 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 799))

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Abstract

In this paper, a mathematical model of synaptic interaction between two pulsed neuron elements is considered. Each of the neurons is represented by a singularly perturbed difference-differential equation with delay. The connection between elements is assumed to be at the threshold, taking into account the time delay. The problems of existence and stability of relaxation cycles are studied. In the framework of the task an algorithm for finding periodic solutions with bursting behavior is proposed. As the delay in the coupling link between the oscillators grows, it is shown that the system exhibits a lot of pulse regimes with different number of spikes over a period length interval. Of particular importance is the fact that the system can have a large number of coexisting relaxation oscillations. The appearance of such bursting effect in the system is a consequence of delay in the coupling link between the oscillators. The obtained result has a natural neurobiological meaning, which is that the growth in the delay leads to an increase in the capacity of this dynamic system as a memory device.

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Acknowledgments

The reported study was funded by RFBR, according to the research project No. 16-31-60039 mol_a_dk.

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Authors and Affiliations

  1. P.G. Demidov Yaroslavl State University, Yaroslavl, Russia

    Elena A. Marushkina

Authors
  1. Elena A. Marushkina
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Correspondence to Elena A. Marushkina .

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Editors and Affiliations

  1. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

    Boris Kryzhanovsky

  2. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

    Witali Dunin-Barkowski

  3. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

    Vladimir Redko

  4. Moscow Aviation Institute (National Research University), Moscow, Russia

    Yury Tiumentsev

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Marushkina, E.A. (2019). Bursting in a System of Two Coupled Pulsed Neurons with Delay. In: Kryzhanovsky, B., Dunin-Barkowski, W., Redko, V., Tiumentsev, Y. (eds) Advances in Neural Computation, Machine Learning, and Cognitive Research II. NEUROINFORMATICS 2018. Studies in Computational Intelligence, vol 799. Springer, Cham. https://doi.org/10.1007/978-3-030-01328-8_40

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