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Mechanism of Appearing Complex Relaxation Oscillations in a System of Two Synaptically Coupled Neurons

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We consider a system of two specially coupled differential-difference equations with delay in the coupling link. We establish that the system has a set of coexisting orbitally asymptotically stable solutions with the total number 2n, n ∈ ℕ, of bursts in the period; moreover, one of the oscillators has m bursts and the other has 2n − m bursts, m = 1, . . . , 2n−1. From the results obtained it follows that an additional delay leads to the appearance of coexisting attractors in the system with a given number of bursts in the period. Bibliography: 20 titles. Illustrations: 2 figures.

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Authors and Affiliations

  1. P. G. Demidov Yaroslavl’ State University 14, Sovetskaya St., Yaroslavl’, 150000, Russia

    S. D. Glyzin & M. M. Preobrazhenskaya

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  1. S. D. Glyzin
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  2. M. M. Preobrazhenskaya
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Correspondence to S. D. Glyzin.

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Translated from Problemy Matematicheskogo Analiza 103, 2020, pp. 71-84.

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Glyzin, S.D., Preobrazhenskaya, M.M. Mechanism of Appearing Complex Relaxation Oscillations in a System of Two Synaptically Coupled Neurons. J Math Sci 249, 894–910 (2020). https://doi.org/10.1007/s10958-020-04982-z

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