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Memristive Hindmarsh-Rose network in 2D lattice with distance-dependent chemical synapses
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DOI：10.1007/s11071-023-08542-3.png)
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Abstract
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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.
Keywords:
Lattice network
Distance-dependent coupling
Stability analysis
Pattern formations
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6
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1.4W
Citations:
4.1W
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