With Smith To Growth In The Population's Economic Capture Model

Firstly the economic harvesting model of Smith increasing is studied in the paper. The conditions for the global stability of the positive equilibrium are obtained by the stability theory of ordinary differential equation and the ecological significances are explained. Then the economic catch model with delay is based on it and the changes of the stability for the positive equilibrium are discussed by the stability theory of differential equation with delay. So we conclude that delay can change the stability of the equilibrium. Lastly a predator-prey system with Smith increasing of prey species is analyzed. The conditions for the global stability of the positive equilibrium are obtained and the existence of a stable periodic solution is proved by ring theory. Considering the harvesting of predator, the economic harvesting model of predator-prey system is established on the above predator-prey system. Then the conditions for the sole existence and global asymptotical stability of the positive equilibrium are gained by the stability theory of ordinary differential equation. To above-mentioned models, we illustrated them by Matlab.