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Front bifurcation in a tristable reaction-diffusion system under periodic forcing.

E P Zemskov1

  • 1Institut für Theoretische Physik, Otto-von-Guericke-Universität, Universitätsplatz 2, 39106 Magdeburg, Germany. zemskov@physik.uni-magdeburg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2004
PubMed
Summary

This study analyzes a tristable reaction-diffusion equation with moving periodic forcing. Periodic forcing alters the front velocity and can lead to multiple solutions and bubble formation in the velocity-phase diagram.

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Area of Science:

  • Applied Mathematics
  • Nonlinear Dynamics
  • Mathematical Physics

Background:

  • Reaction-diffusion equations model phenomena across various scientific disciplines.
  • Tristable systems exhibit complex dynamic behaviors, including multiple stable states.
  • External forcing can significantly alter the dynamics of traveling waves.

Purpose of the Study:

  • To investigate the effects of moving periodic external forcing on a piecewise linear tristable reaction-diffusion equation.
  • To analytically derive front velocity equations and analyze the conditions for front existence.
  • To explore the impact of forcing on the phase-dependent behavior and velocity bifurcation of traveling fronts.

Main Methods:

  • Analytical derivation of front velocity equations using matching procedures for front solutions.

Related Experiment Videos

  • Analysis of null-cline structure and interfacial zone constraints for front existence.
  • Investigation of the velocity-versus-phase diagram under periodic forcing.

    • Main Results:

    • Front velocity equations were obtained analytically, revealing constraints on the null-cline structure.
    • The existence of a set of front solutions with varying phases was demonstrated in the presence of forcing.
    • Periodic forcing modifies the velocity-phase diagram, leading to bubble formation and additional solutions for specific wave numbers.

    Conclusions:

    • Moving periodic forcing introduces complex behaviors in tristable reaction-diffusion systems, including multiple phase-dependent solutions.
    • The analysis highlights critical conditions for the existence of traveling fronts under such forcing.
    • The study reveals novel phenomena like bubble formation in the velocity-phase diagram, indicating bifurcations to multiple fronts.