Computation of the response functions of spiral waves in active media

Abstract

Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. A small perturbation causes gradual change in spatial location of spiral's rotation center and frequency, i.e. drift. The response functions (RFs) of a spiral wave are the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues $\lambda =0,\pm i\omega$. The RFs describe the spiral's sensitivity to small perturbations in the way that a spiral is insensitive to small perturbations where its RFs are close to zero. The velocity of a spiral's drift is proportional to the convolution of RFs with the perturbation. Here we develop a regular and generic method of computing the RFs of stationary rotating spirals in reaction-diffusion equations. We demonstrate the method on the FitzHugh-Nagumo system and also show convergence of the method with respect to the computational parameters, i.e. discretization steps and size of the medium. The obtained RFs are localized at the spiral's core.

10 pages, 5 figures, as accepted to Phys Rev E 2009/04/03

References in corpus (3)

• Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states
• Spiral wave drift in an electric field and scroll wave instabilities
• Computation of Spiral Spectra

Cited by in corpus (24)

• Computation of the Drift Velocity of Spiral Waves using Response Functions
• Drift Laws for Spiral Waves on Curved Anisotropic Surfaces
• Collective phase description of oscillatory convection
• A Simple Model for Identifying Critical Structures in Atrial Fibrillation
• Buckling of scroll waves
• Drift of scroll waves in thin layers caused by thickness features: asymptotic theory and numerical simulations
• Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone
• Three-Dimensional Autonomous Pacemaker in the Photosensitive Belousov-Zhabotinsky medium
• Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation
• Exact Coherent Structures and Chaotic Dynamics in a Model of Cardiac Tissue
• Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field
• Non-specular reflections in a macroscopic system with wave-particle duality: spiral waves in bounded media
• Unstable Spiral Waves and Local Euclidean Symmetry in a Model of Cardiac Tissue
• Alternative Stable Scroll Waves and Conversion of Autowave Turbulence
• Effective dynamics of twisted and curved scroll waves using virtual filaments
• Front propagation in three-dimensional corrugated reaction-diffusion media
• Asymptotic dynamics of reflecting spiral waves
• Subcritical Hopf Bifurcations in the FitzHugh-Nagumo Model
• A response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves
• Filament tension and phase-locked drift of meandering scroll waves
• Phase and amplitude description of complex oscillatory patterns in reaction-diffusion systems
• Scroll Waves and Filaments in excitable Media of higher spatial Dimension
• Dynamics of wave fronts and filaments in anisotropic cardiac tissue
• Pulsating and rotating spirals in a delayed feedback diffractive nonlinear optical system