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Dynamics of unidirectionally-coupled ring neural network with discrete and distributed delays

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Abstract

In this paper, we consider a ring neural network with one-way distributed-delay coupling between the neurons and a discrete delayed self-feedback. In the general case of the distribution kernels, we are able to find a subset of the amplitude death regions depending on even (odd) number of neurons in the network. Furthermore, in order to show the full region of the amplitude death, we use particular delay distributions, including Dirac delta function and gamma distribution. Stability conditions for the trivial steady state are found in parameter spaces consisting of the synaptic weight of the self-feedback and the coupling strength between the neurons, as well as the delayed self-feedback and the coupling strength between the neurons. It is shown that both Hopf and steady-state bifurcations may occur when the steady state loses stability. We also perform numerical simulations of the fully nonlinear system to confirm theoretical findings.

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Authors and Affiliations

  1. Mathematics Unit, School of Science and Engineering, University of Kurdistan Hewlêr (UKH), Erbil, Kurdistan Region, Iraq

    Bootan Rahman

  2. Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK

    Yuliya N. Kyrychko & Konstantin B. Blyuss

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  1. Bootan Rahman
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  2. Yuliya N. Kyrychko
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  3. Konstantin B. Blyuss
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Correspondence to Bootan Rahman.

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Rahman, B., Kyrychko, Y.N. & Blyuss, K.B. Dynamics of unidirectionally-coupled ring neural network with discrete and distributed delays. J. Math. Biol. 80, 1617–1653 (2020). https://doi.org/10.1007/s00285-020-01475-0

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