Starvation-driven diffusion in predator-prey dynamics.

Area of Science:

• Mathematical Biology
• Ecology
• Dynamical Systems

Background:

• Starvation driven diffusion (SDD) is a behavioral strategy where species increase movement when facing starvation.
• Predator-prey systems are fundamental ecological models, but the impact of SDD on both predator and prey has been less explored.

Purpose of the Study:

• To investigate the stability and coexistence conditions in predator-prey systems where both species exhibit SDD.
• To analyze the emergence and characteristics of non-trivial steady states and spatio-temporal dynamics using bifurcation theory.

Main Methods:

• Linearized eigenvalue problem analysis for steady-state stability.
• Crandall-Rabinowitz and global bifurcation theorems for analyzing steady-state bifurcations.
• Application to predator-prey models with Holling type II/IV functional responses.
• Numerical simulations to verify theoretical findings and observe complex dynamics.

Main Results:

• The stability of the semi-trivial steady state depends on conversion efficiency and predator motility.
• Coexistence is possible when the semi-trivial state is unstable.
• A critical conversion efficiency triggers steady-state bifurcation, leading to non-trivial solutions.
• Spatially inhomogeneous periodic solutions were observed, mirroring resource distribution.

Conclusions:

• SDD significantly influences predator-prey dynamics, affecting stability and coexistence.
• Bifurcation theory provides insights into the emergence of complex population distributions.
• Observed solutions align with the ideal free distribution, suggesting adaptive movement strategies under resource scarcity.