scholarly journals Computation of the response functions of spiral waves in active media

2009 ◽  
Vol 79 (5) ◽  
Author(s):  
I. V. Biktasheva ◽  
D. Barkley ◽  
V. N. Biktashev ◽  
G. V. Bordyugov ◽  
A. J. Foulkes
Keyword(s):  
Spiral Waves ◽  
Response Functions ◽  
Active Media

scholarly journals LOCALIZATION OF RESPONSE FUNCTIONS OF SPIRAL WAVES IN THE FITZHUGH–NAGUMO SYSTEM

2006 ◽  
Vol 16 (05) ◽  
pp. 1547-1555 ◽  
Author(s):  
I. V. BIKTASHEVA ◽  
A. V. HOLDEN ◽  
V. N. BIKTASHEV
Keyword(s):  
External Force ◽  
Wave Solution ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Response Functions ◽  
Space And Time ◽  
Wave Drift ◽  
Linearized Problem ◽  
Small Periodic

Dynamics of spiral waves in perturbed, e.g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spirals Response Functions, which are eigenfunctions of the adjoint linearized problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh–Nagumo model, and show that they are effectively localized in the vicinity of the spiral core.

scholarly journals Computation of the drift velocity of spiral waves using response functions

2010 ◽  
Vol 81 (6) ◽  
Author(s):  
I. V. Biktasheva ◽  
D. Barkley ◽  
V. N. Biktashev ◽  
A. J. Foulkes
Keyword(s):  
Drift Velocity ◽  
Spiral Waves ◽  
Response Functions

Kinematical Description of Meandering Spiral Waves in Active Media

2002 ◽  
Vol 216 (5) ◽  
Author(s):  
M. Braune ◽  
H. Engel
Keyword(s):  
Boundary Condition ◽  
Spiral Waves ◽  
Rigid Rotation ◽  
Active Media ◽  
Curvature Effects ◽  
Kinematical Approach

Under certain conditions the dynamics of spiral waves in active media can be described within a kinematical approach. We discuss the importance of curvature effects for the transition from rigidly rotating to outward meandering spirals. To include these effects into the kinematical description we propose a modified boundary condition for the curvature at the tip. This allows to recover a variety of rotation regimes with hypocycloid-like trajectories of the spiral tip corresponding to outward meandering spiral waves which are frequently observed experimentally in active media of quite different nature beyond the instability of rigid rotation.

scholarly journals Nonlinear Concave Spiral Waves in Active Media Transferring Energy

2019 ◽  
Vol 224 ◽  
pp. 02011
Author(s):  
Mikhail Mazurov
Keyword(s):  
Mathematical Model ◽  
Breaking Waves ◽  
Spiral Waves ◽  
Computational Experiments ◽  
Active Media ◽  
Nagumo Equation

Spiral concave autowaves are widely implemented in physics, chemistry, hydrodynamics, meteorology and other fields. A mathematical model of spiral concave autowaves based on the Fitzhugh-Nagumo equation and modified axiomatic models are presented. The existence of spiral concave autowaves transferring energy was predicted via computational experiments. Applications of spiral concave autowaves carrying energy in hydrodynamics, generation of tornadoes, breaking waves, and tsunamis and examples of such autowaves in biology and medicine are reviewed and the importance of concave spiral autowaves transferring energy is emphasized.

Spiral waves in active media

1984 ◽  
Vol 27 (9) ◽  
pp. 783-793 ◽  
Author(s):  
V. I. Krinskii ◽  
A. S. Mikhailov ◽  
A. V. Panfilov ◽  
E. A. Ermakova ◽  
M. A. Tsyganov
Keyword(s):  
Spiral Waves ◽  
Active Media
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