| Abstract: |
| This talk studies a spatial prey-predator model incorporating protection zone for prey and directed predator flux toward high-prey-density regions. We investigate how the interaction between spatial refuge and directed movement influences qualitative structures of solutions. In particular, we analyze bifurcation structures of positive stationary solutions and describe their behavior as the directed flux becomes large. The analysis reveals saddle-node bifurcations and multiplicity of coexistence states generated by the combined effects of protection zone and directed flux. We also discuss the associated nonstationary problem and explain how solvability can be established despite discontinuities arising from the refuge interface. These results clarify how protection mechanism and directed flux jointly organize solution structures in prey-predator systems. |
|