Turing instability induced by random network in FitzHugh-Nagumo model

Qianqian Zheng and Jianwei Shen

Applied Mathematics and Computation, 2020, vol. 381, issue C

Abstract: Although there is general agreement that the network plays an essential role in the biological system, how the connection probability of network affects the natural model(Especially neural network) is poorly understood. In this paper, we show the impact of the network on Turing instability in the FitzHugh-Nagumo(FN) model. Then we obtain the condition of how the Turing bifurcation, saddle-node bifurcation, and Turing instability occur. By using the Gershgorin circle theorem, we investigate the relationship between degree and eigenvalue of the network matrix, and obtain the approximate range of eigenvalue of the network matrix. Also, We derive the instability condition about diffusion and the connection probability in the network-organized system. And then we obtain the estimated range of connection probability. Meanwhile we apply these results to explaining the spiking of neuron and find this system has rich dynamics behavior. Finally, the numerical simulation verifies our analytical results.

Keywords: Turing instability; Pattern formation; Random network; Connection probability (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302708

DOI: 10.1016/j.amc.2020.125304

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