Edge of Chaos in Integro-Differential Model of Nerve Conduction

Ravi Agarwal, Alexander Domoshnitsky, Angela Slavova () and Ventsislav Ignatov
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Ravi Agarwal: Department of Mathematics, Texas A&M University Kingsville, Kingsville, TX 78363, USA
Alexander Domoshnitsky: Department of Mathematics, Ariel University, Ariel 40700, Israel
Angela Slavova: Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Ventsislav Ignatov: Laboratory of Engineering Mathematics, Ruse University “Angel Kanchev”, 7017 Ruse, Bulgaria

Mathematics, 2024, vol. 12, issue 13, 1-12

Abstract: In this paper, we consider an integro-differential model of nerve conduction which presents the propagation of impulses in the nerve’s membranes. First, we approximate the original problem via cellular nonlinear networks (CNNs). The dynamics of the CNN model is investigated by means of local activity theory. The edge of chaos domain of the parameter set is determined in the low-dimensional case. Computer simulations show the bifurcation diagram of the model and the dynamic behavior in the edge of chaos region. Moreover, stabilizing control is applied in order to stabilize the chaotic behavior of the model under consideration to the solutions related to the original behavior of the system.

Keywords: integro-differential model; nerve conduction; local activity; edge of chaos; stabilizing control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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