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The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Speed of traveling fronts in a sigmoidal reaction-diffusion system
E P Zemskov1, K Kassner, M A Tsyganov
1Department of Chemistry, Brandeis University, Waltham, Massachusetts 02454, USA. zemskov@brandeis.edu
Chaos (Woodbury, N.Y.)
|April 5, 2011
Summary
This study explores a modified FitzHugh-Nagumo model, revealing novel wave front dynamics and bifurcations with one, three, or five fronts. These findings offer new insights into reaction-diffusion systems.
Area of Science:
- Computational Neuroscience
- Mathematical Biology
- Chemical Kinetics
Background:
- The FitzHugh-Nagumo model is a cornerstone for studying excitable media dynamics.
- Reaction-diffusion systems are crucial for understanding phenomena like signal propagation.
- Classical models often exhibit limited wave front behaviors.
Purpose of the Study:
- To analyze the dynamics of wave fronts in a sigmoidal FitzHugh-Nagumo reaction-diffusion system.
- To investigate bifurcations and the number of wave fronts based on model parameters.
- To explore the stability of complex front solutions.
Main Methods:
- Analytic description using piecewise linear approximations for reaction kinetics.
- Complete characterization of wave front dynamics.
- Numerical investigation of front stability.
Main Results:
- Identified significant front bifurcations leading to one, three, or five fronts.
- Demonstrated variations in front number and speed with model parameters.
- Observed and analyzed the stability of five-front solutions.
Conclusions:
- The sigmoidal FitzHugh-Nagumo model exhibits richer wave front dynamics than the classical model.
- Parameter variations critically influence the number and speed of wave fronts.
- The study provides a comprehensive understanding of bifurcations in this reaction-diffusion system.
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