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Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.
Evgeny P Zemskov1, Mikhail A Tsyganov2, Werner Horsthemke3
1Federal Research Center for Computer Science and Control, Russian Academy of Sciences, Vavilova 40, 119333 Moscow, Russia.
Physical Review. E
|February 18, 2017
Summary
Cross diffusion in the FitzHugh-Nagumo model generates solitary pulses and wave trains, unlike standard systems. This reaction-diffusion study reveals new wave behaviors driven by cross diffusion.
Area of Science:
- Computational neuroscience
- Mathematical biology
- Chemical kinetics
Background:
- The FitzHugh-Nagumo model is a simplified model of neuron action potentials.
- Reaction-diffusion systems are used to model phenomena like pattern formation and wave propagation.
- Cross diffusion introduces coupling between different species or components in a diffusion process.
Purpose of the Study:
- To investigate the behavior of traveling waves in a reaction-diffusion system with linear cross diffusion.
- To analyze the impact of cross diffusion on wave profiles and propagation speed.
- To explore wave phenomena in a piecewise linear approximation of the FitzHugh-Nagumo model.
Main Methods:
- Utilizing a piecewise linear approximation of the FitzHugh-Nagumo model.
- Analyzing homoclinic solutions for solitary pulses.
- Analyzing periodic solutions for wave trains.
- Examining the effects of linear cross diffusion on wave dynamics.
Main Results:
- The presence of cross diffusion leads to the emergence of both solitary pulses and wave trains.
- In contrast, standard bistable systems without cross diffusion only exhibit fronts.
- Cross diffusion significantly affects the profiles and speeds of these traveling waves.
Conclusions:
- Cross diffusion introduces novel wave behaviors, including pulses and wave trains, in the FitzHugh-Nagumo model.
- This finding expands the understanding of wave dynamics in reaction-diffusion systems.
- The study highlights the crucial role of cross diffusion in shaping complex spatiotemporal patterns.
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