Global dynamics of a Lotka-Volterra type prey–predator model with diffusion and predator-taxis

Abstract

This paper studies a reaction–advection–diffusion prey–predator system in one spatial dimension. Adapting the Lotka–Volterra-type functional response, we prove the global existence and boundedness of solutions of the system in a bounded open interval. In view of asymptotic behavior of solutions, we show that if the predation is weak, the semi-trivial steady state at which prey only survive is globally asymptotically stable. In case of strong predation, the positive steady state is globally asymptotically stable when the predator-taxis is weak.

2010 Mathematics Subject Classification:

• 23783

Acknowledgments

The author is very grateful to the anonymous referee for careful reading and valuable suggestions. The research was supported by National Research Foundation of Korea (NRF) under contract numbers NRF-2017R1D1A1B03031035 and NRF-2020R1I1A1A01074337.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was supported by National Research Foundation of Korea (NRF) under contract numbers NRF-2017R1D1A1B03031035 and NRF-2020R1I1A1A01074337.