The effect of initial values on extinction or persistence in degenerate diffusion competition systems

Area of Science:

• Mathematical Biology
• Ecology
• Dynamical Systems

Background:

• Classical Lotka-Volterra competition diffusion systems show asymptotic spreading independent of initial values.
• Species extinction or persistence is solely determined by kinetic system dynamics.

Purpose of the Study:

• Investigate the influence of initial values on degenerate competition diffusion systems with a weak Allee effect.
• Demonstrate how initial conditions can induce rich dynamics, altering extinction and persistence outcomes.

Main Methods:

• Analysis of degenerate competition diffusion systems.
• Exploration of the interplay between nonlinear reaction, diffusion, and initial conditions.
• Examination of Allee effect impacts on species dynamics.

Main Results:

• Initial values can dictate species extinction or persistence, even when the kinetic system is fixed.
• Observed four distinct spreading-vanishing phenomena based on initial conditions.
• Demonstrated that the superior competitor can be eliminated by the inferior competitor due to initial habitat size and Allee effect intensity.

Conclusions:

• Initial conditions play a crucial role in determining species' fate in degenerate competition diffusion systems.
• The Allee effect, combined with initial conditions, can reverse competitive hierarchies.
• Findings highlight the importance of considering initial states in ecological modeling.