Existence of Positive Steady-state Solution of a Predator-prey Dynamics with Dinosaur Functional Response and Heterogeneous Environment.

It is well known that the effects of the protection zone on the dynamical behavior are significantly different from the non-protection zone. In this paper, we presents a semi-linear ellipic system, which describes the predator-prey relationship with Dinosaur functional response under homogeneous Neumann boundary conditions. This paper concerns the existence of non-constant positive steady-state solutions, in the case (1): Nondegeneracy of β(x) with β(x) > 0 on Ω or case (2): Degeneracy of β(x) with β(x) = 0 in Ω0, β(x) > 0 in Ω \ Ω0. These results provide theoretical evidence for the complex spatiotemporal dynamics. [ABSTRACT FROM AUTHOR]