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ABSTRACT
This paper is concerned with the global dynamics of a ratio-dependent predator–prey system with prey-taxis. We establish the global existence and uniform-in-time boundedness of solutions in any dimensional bounded domain with Neumann boundary conditions, and furthermore prove the global stability of homogeneous steady states under certain conditions. Finally we perform numerical simulations to show that the pattern formation may arise and prey-taxis is a factor driving the evolution of spatial inhomogeneity into homogeneity.
Acknowledgments
The authors thanks the two referees for very helpful comments which lead to an improvement of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The research of Y. Cai was supported by the National Natural Science Foundation of China [11601179 and 61672013]. The research of Z. A. Wang was partially supported by Research Grants Council, University Grants Committee GRF grant PolyU 153298/16P (Project ID P0005162).