Analyzing critical propagation in a reaction-diffusion-advection model using unstable slow waves

Area of Science:

• Mathematical modeling
• Theoretical physics
• Chemical kinetics

Background:

• Reaction-diffusion models describe wave propagation.
• Previous studies focused on stable fast waves and advection effects.
• The influence of advection on unstable slow waves was less understood.

Purpose of the Study:

• To investigate the effect of advection on traveling wave propagation and critical speed in reaction-diffusion models.
• To derive an analytical expression for the advection-velocity relation of unstable slow waves.
• To determine the critical advection strength supporting wave propagation.

Main Methods:

• Analytical derivation of advection-velocity relation for unstable waves.
• Numerical analysis of a two-variable reaction-diffusion-advection model.
• Comparison of theoretical predictions with numerical results.

Main Results:

• An analytical expression for the advection-velocity relation of unstable slow waves was derived.
• The critical advection strength was calculated, considering the unstable slow wave solution.
• Stable wave propagation was observed in non-excitable regimes above a critical advection strength.

Conclusions:

• Theoretical predictions for critical advection strength align well with numerical results.
• Advection can stabilize wave propagation in parameter regimes where it would otherwise cease.
• The study provides a theoretical explanation for observed wave behaviors under advection.