Two Results About Recovery Rate Of The Two-species Predator-prey System

In natural ecological systems, the relationship of the two-species predator-prey is a basic species interaction. Transitions in ecological systems often occur without apparent warning, and the decreasing of the recovery rate is a good warning single of the critical transition.Fistly, based on the detailed derivation and analysis to the theory and numerical examples of the predator-prey model studied by Chisholm, R. A. and Filotas, E., this article defines a kind of the predator-prey model with constant stocking rate of the prey, and studies the relationship of the recovery rate and the carrying capacity of the prey as well as the effects of the stocking rate on the recovery rate and warning length. Finally, analyzes the relation between the decreasing recovery rate as a indicator of the system shift and the stocking rate and the carrying capacity of the prey by examples via Matlab. The results showe that the stocking prey can increase effects of the warning and the model has practical ecological significance.Secondly, based on the predator-prey model whose functional reaction function only considers the prey population studied by Chisholm, R. A. and Filotas, E., this article proposes a kind of predator-prey model based on the condition that predator-prey capture rate affected by the carring capacity of prey, and studies the relationship of the recovery rate and the carrying capacity of the prey. Finally, this article analyzes the relation between the decreasing recovery rate as a indicator of the system shift via Matlab. The results showe that this model has a better practical significance in the practical ecosystems.