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Semi-analytical Approach to Criteria for Ignition of Excitation Waves by Bezekci, B.; Idris, I.; Simitev, R. D.; Biktashev, V. N. is a scholarly article available to read on EtoBox.

What is Semi-analytical Approach to Criteria for Ignition of Excitation Waves about?

We consider the problem of ignition of propagating waves in one-dimensional bistable or excitable systems by an instantaneous spatially extended stimulus. Earlier we proposed a method (Idris and Biktashev, PRL, vol 101, 2008, 244101) for analytical description of the threshold conditions based on an approximation of the (center-)stable manifold of a certain critical solution. Here we generalize this method to address a wider class of excitable systems, such as multicomponent reaction-diffusion systems and systems with non-self-adjoint linearized operators, including systems with moving critical fronts and pulses. We also explore an extension of this method from a linear to a quadratic approximation of the (center-)stable manifold, resulting in some cases in a significant increase in accuracy. The applicability of the approach is demonstrated on five test problems ranging from archetypal examples such as the Zeldovich--Frank-Kamenetsky equation to near realistic examples such as the Beeler-Reuter model of cardiac excitation. While the method is analytical in nature, it is recognised that essential ingredients of the theory can be calculated explicitly only in exceptional cases, so w

Author

Bezekci, B.; Idris, I.; Simitev, R. D.; Biktashev, V. N.

Published

2015

Language

EN