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Updated: Jul 4, 2026
08:32
External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
Published on: May 7, 2017
Wavy fronts and speed bifurcation in excitable systems with cross diffusion
E P Zemskov1, K Kassner, M J B Hauser
1Computing Centre of the Russian Academy of Sciences, Moscow, Russia. zemskov@ccas.ru
Summary
Researchers discovered a new bifurcation of excitation fronts in activator-inhibitor systems. This phenomenon, similar to the Ising-Bloch bifurcation, leads to novel front types with oscillating tails.
Area of Science:
- Nonlinear Dynamics
- Chemical Kinetics
- Mathematical Biology
Background:
- Reaction-diffusion systems are fundamental models in various scientific fields.
- Bistable systems exhibit multiple stable states, leading to complex dynamics.
- Activator-inhibitor systems are crucial for understanding pattern formation.
Purpose of the Study:
- To discover and characterize a novel bifurcation of excitation fronts.
- To investigate the role of cross-diffusion in two-component bistable systems.
- To analyze the properties of fronts associated with this bifurcation.
Main Methods:
- Analysis of two-component bistable reaction-diffusion systems.
- Investigation of cross-diffusion effects.
- Derivation of exact analytical solutions for piecewise linear models.
Main Results:
- Discovery of a bifurcation of excitation fronts, analogous to the nonequilibrium Ising-Bloch bifurcation.
- Identification of a new class of fronts with oscillating spatial profiles.
- Exact analytical solutions were obtained for these novel fronts.
Conclusions:
- Cross-diffusion can induce significant bifurcations in reaction-diffusion systems.
- The discovered bifurcation offers new insights into front dynamics.
- The analytical solutions provide a foundation for further theoretical and experimental studies.
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