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Scroll waves in isotropic excitable media: linear instabilities, bifurcations, and restabilized states
1Laboratoire de Physique Statistique, Associé au CNRS et aux Universités Paris VI et VII, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France.
Summary
This study analyzes scroll waves in excitable media, revealing how different parameter regions lead to instabilities. These findings help understand complex wave dynamics and deformations in three-dimensional systems.
Area of Science:
- Theoretical physics
- Computational biology
- Chemical kinetics
Background:
- Scroll waves are complex 3D wave phenomena in excitable media.
- Understanding their stability is crucial for modeling biological and chemical systems.
- Previous studies often focused on 2D spiral waves.
Purpose of the Study:
- To compute the linear stability spectrum of untwisted and twisted scroll waves.
- To characterize bifurcations and resulting states using numerical simulations.
- To analyze long-wavelength deformations via adjoint eigenmodes.
Main Methods:
- Linear stability analysis of a two-variable reaction-diffusion model.
- Direct numerical simulations of scroll wave dynamics.
- Computation of adjoint linear stability operator eigenmodes.
Main Results:
- Identified distinct bands of unstable modes across different parameter spaces.
- Characterized bifurcations and emergent complex states.
- Quantified scroll wave deformations using matrix elements from adjoint computations.
Conclusions:
- Scroll wave stability is highly dependent on parameter regimes.
- Numerical simulations and adjoint analysis provide comprehensive insights into wave behavior.
- This work advances the understanding of complex spatiotemporal patterns in excitable media.