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Memristive Hindmarsh-Rose network in 2D lattice with distance-dependent chemical synapses

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Abstract

In this work, the synchronisation scenario and pattern formations are analysed in a network of modified Hindmarsh-Rose neurons arranged in a two-dimensional lattice. The coupling between neurons is nonlinear in nature and takes into account the distance between the neurons that form a square around it. The power law exponent strengthens the distance dependence. The study is carried out by varying coupling strength, distance dependence and coordination number. As the strength of the distance dependence of coupling increases, synchrony attains at a higher coupling strength. The analysis of the synchronisation scenario indicates that the synchronisation within a group is low and the synchrony between groups is high. The coupling threshold for attaining synchrony is determined by the coordination number and is not affected by the size of the network. As the coordination number increases, the synchrony attains at a weaker coupling strength. The stability of the synchrony is quantified using the Lyapunov function approach. Each group responds differently to the same coupling strength and the network shows interesting spatiotemporal patterns. The emergence of chimera and multichimera states is quantified using the strength of incoherence and discontinuity measure. This work sheds light on the coordination between and within layers of a complex system, including how different layers have unique responses to the same input. It also helps to understand how the interplay between coupling strength and distance dependence leads to the formation of interesting patterns.

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Data availability

The data that support the findings were generated from numerical simulations by the software MATLAB.

Code availability

Code for data simulation was developed by ourselves in MATLAB and will be made available on request.

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Acknowledgements

TR would like to thank UGC, India, for the research fellowship through MANF, and PAS would like to acknowledge DST, India, for the financial assistance through FIST program.

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  1. Department of Physics, Farook College, University of Calicut, Malappuram, Kerala, 673632, India

    T. Remi & P. A. Subha

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  1. T. Remi
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Both authors contributed to the study, conception and design. The work, data simulation and analysis were performed by T. Remi. P. A. Subha made substantial contributions to the conception or design of the work.

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Correspondence to P. A. Subha.

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Remi, T., Subha, P. . Memristive Hindmarsh-Rose network in 2D lattice with distance-dependent chemical synapses. Nonlinear Dyn 111, 14455–14466 (2023). https://doi.org/10.1007/s11071-023-08542-3

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