Shaping wave patterns in reaction-diffusion systems
arXiv:1405.4321 · doi:10.1103/PhysRevE.90.062911
Abstract
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, as e.g. interfaces and excitation pulses. Control signals that realize a pre-given wave shape are determined analytically from nonlinear evolution equation for isoconcentration lines as the perturbed nonlinear phase diffusion equation or the perturbed linear eikonal equation. While the control enforces a desired wave shape perpendicular to the local propagation direction, the wave profile along the propagation direction itself remains almost unaffected. Provided that the one-dimensional wave profile and its propagation velocity can be measured experimentally, and the diffusion coefficients of the reacting species are given, the new approach can be applied even if the underlying nonlinear reaction kinetics are unknown.
12 pages, 4 figures
References in corpus (7)
- A reaction-diffusion model for the growth of avascular tumor
- Biscale Chaos in Propagating Fronts
- Controlling the position of traveling waves in reaction-diffusion systems
- Propagation Of Waves In Periodic-Heterogeneous Bistable Systems
- Crystal growth as an excitable medium
- Control of chemical wave propagation
- Stability of position control of traveling waves in reaction-diffusion systems