Front dynamics in a two-species competition model driven by Lévy flights

Area of Science:

• Ecology
• Mathematical Biology
• Physics

Background:

• Many species exhibit Lévy random walk foraging, which is more efficient than Brownian motion in scarce environments.
• Existing diffusion-reaction models often fail to incorporate the superdiffusive population spread characteristic of Lévy flights.

Purpose of the Study:

• To develop and analyze a novel diffusion-reaction model for competing species employing Lévy flights.
• To investigate the impact of fractional-order diffusion on population spread dynamics.

Main Methods:

• Modified the Lotka-Volterra equations by replacing the standard second-order diffusion operator with a fractional-order one.
• Employed theoretical analysis and numerical simulations to study population front propagation.

Main Results:

• Fractional-order diffusion accelerates population fronts exponentially and causes a power-law decay in the leading tail.
• Derived conditions for front "catch-up" based on the fractional derivative's skewness.

Conclusions:

• Standard second-order diffusion models are inadequate for species exhibiting Lévy flight behavior.
• The proposed fractional-order diffusion model provides a more accurate representation of superdiffusive population spread, crucial for ecological simulations.