Complex dynamics in a nerve fiber model with periodic coefficients

2007/08/17 by Chiara Zanini, Zanini, Chiara, Fabio Zanolin +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #math.DS

paper · pdf · doi:10.48550/arxiv.0708.2342

29 pages, 5 figures

arxiv created 2007/08/17 · openalex publication_date 2007/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deal with the periodic boundary value problem for a second-order nonlinear ODE which includes the case of the Nagumo type equation v_xx - g v + n(x) F(v) = 0, previously considered by Grindrod and Sleeman and by Chen and Bell in the study of nerve fiber models. In some recent works we discussed the case of nonexistence of nontrivial solutions as well as the case in which many positive periodic solutions may arise, the different situations depending by threshold parameters related to the weight function n(x). Here we show that for a step function n(x) (or for small perturbations of it) it is possible to obtain infinitely many periodic solutions and chaotic dynamics, due to the presence of a topological horseshoe (according to Kennedy and Yorke).

Citations

• On the bifurcation curve for an elliptic system of FitzHugh–Nagumo type
• Multipeak solutions for an elliptic system of Fitzhugh-Nagumo type

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