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Targeting characteristic wave properties in reaction-diffusion systems by optimization of external forcing
Jochen Siehr1, Mario S Mommer, Oliver Slaby
1Interdisciplinary Center for Scientific Computing, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
Summary
This study optimizes external forcing to precisely control reaction-diffusion waves, like wavelength and speed. The method, demonstrated on the FitzHugh-Nagumo system, offers a general approach for manipulating wave dynamics.
Area of Science:
- Nonlinear dynamics
- Mathematical biology
- Computational physics
Background:
- Reaction-diffusion systems generate complex spatio-temporal patterns.
- Controlling these wave dynamics is crucial for understanding biological processes and designing artificial systems.
- External forcing offers a means to influence these patterns.
Purpose of the Study:
- To develop a method for targeted manipulation of reaction-diffusion waves.
- To optimize external forcing parameters to control specific wave properties.
- To demonstrate the applicability of the method to the FitzHugh-Nagumo system.
Main Methods:
- Model-based optimization of external forcing parameters.
- Optimal control of periodic orbits in a wave-variable coordinate system.
- Numerical simulations of the FitzHugh-Nagumo system with spatiotemporally controlled electric current.
Main Results:
- Successfully targeted characteristic wave properties including wavelength, shape, and propagation speed.
- Validated the optimal control approach through numerical simulations.
- Demonstrated precise control over reaction-diffusion wave dynamics.
Conclusions:
- The proposed method enables targeted manipulation of reaction-diffusion waves.
- The approach is based on optimal control principles and applicable to various reaction-diffusion models.
- This provides a powerful tool for controlling complex wave phenomena.
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