This paper is concerned with a diffusive Lotka-Volterra prey-predator model with finitely many protection zones for the prey species. We discuss the stability of trivial and semi-trivial steady-state solutions, and we also study the existence and non-existence of positive steady-state solutions. It is proved that there exists a certain critical growth rate of the prey for survival. Moreover, it is shown that when cross-diffusion is present, under certain conditions, the critical value decreases as the number of protection zones increases. On the other hand, it is also shown that when cross-diffusion is absent, the critical value does not always decrease even if the number of protection zones increases.
|Number of pages||20|
|Journal||SUT Journal of Mathematics|
|Publication status||Published - 2017 Jan 1|
- Prey-predator model
- Protection zone
ASJC Scopus subject areas