Boundedness and global stability of a diffusive prey–predator model with prey-taxis

ABSTRACT

A diffusive prey–predator model with prey-taxis and trophic interactions of three levels is proposed and analyzed, in which the predator could move in the direction of prey gradient. We prove the global existence and boundedness of solutions of the system on bounded domains with no-flux boundary condition. The result holds for arbitrary spatial dimension and any prey-taxis sensitivity coefficient. Moreover, we also prove that such prey-taxis does not qualitatively affect the existence and stability of nonnegative equilibria under some conditions.

Keywords:

• Prey–predator model
• prey-taxis
• trophic function
• global existence
• global stability

2010 MSC:

• 35A01
• 35K59
• 92D25
• 35B45
• 92C17

Acknowledgments

The author would like to thank the anonymous referee for the helpful constructive comments of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by National Natural Science Foundation of China [grant number 11901310], Natural Science Foundation of Jiangsu Province of China [grant number BK20180737], Natural Science Foundation for Colleges and Universities in Jiangsu Province [grant number 18KJB110023], and Nanjing University of Posts and Telecommunications Science Foundation [grant numbers NY218130 and NY219064].