Positive periodic solutions of a Hassell-Varley type predator-prey system (Q2254403)

For the ratio-dependent predator-prey reaction-diffusion system with Hassell-Varley functional responde, governed by the nonlinear parabolic system in a bounded domain \(\Omega\) with Robin or Dirichlet boundary conditions, necessary and sufficient conditions for the existence of time-periodic positive solutions are obtained by using fixed point index theory, and their asymptotic behavior is investigated. For the relevant steady-state problem, also the existence of positive solutions is proved. In the conclusion, the biological treatment of the obtained results is given.