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On propagation failure in one- and two-dimensional excitable media
Georg A Gottwald1, Lorenz Kramer
1School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia. gottwald@maths.usyd.edu.au
Chaos (Woodbury, N.Y.)
|September 28, 2004
Summary
We developed a new nonperturbative technique to analyze pulse dynamics in excitable media. This method accurately predicts pulse behavior and failure points in both 1D and 2D systems, matching simulation results.
Area of Science:
- Physics
- Nonlinear Dynamics
- Mathematical Biology
Background:
- Excitable media exhibit complex pulse dynamics.
- Understanding pulse propagation failure is crucial in various scientific fields.
- Existing methods may lack accuracy for nonperturbative analyses.
Purpose of the Study:
- To introduce a novel nonperturbative technique for studying pulse dynamics.
- To analyze pulse propagation failure in one- and two-dimensional excitable media.
- To derive approximate expressions for pulse characteristics and scaling behavior.
Main Methods:
- Development of a nonperturbative analytical technique.
- Application of the method to one-dimensional pulse dynamics near saddle node bifurcation.
- Generalization of the method to two-dimensional systems to study broken front retraction.
- Comparison with results from numerical simulations.
Main Results:
- Accurate description of pulse and wave train behavior near propagation failure in 1D.
- Successful capture of broken front retraction dynamics in 2D.
- Derivation of approximate expressions for pulse shape, velocity, and scaling.
- Good agreement between analytical results and numerical simulations.
Conclusions:
- The presented nonperturbative technique is effective for studying pulse dynamics in excitable media.
- The method provides valuable insights into propagation failure mechanisms.
- The findings are validated by numerical simulations, showing the technique's robustness.
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