Dynamics analysis of a pest management prey–predator model by means of interval state monitoring and control. (February 2017) - Tian, Yuan; Zhang, Tonghua; Sun, Kaibiao
Abstract: In this work, a new pest management strategy by means of interval state monitoring is introduced into a prey–predator model, i.e. when the pest density exceeds the slightly harmful level but is below the damage level, the biological control is adopted in case of the predator density below a maintainable level, once the pest density exceeds the damage level, the chemical control is adopted. In order to determine the frequency of the chemical control and yield of releases of the predator, analysis on the existence of order-1 or order-2 periodic orbit is carried out by the construction of Poincaré map. The results could make the pest control strategy to be a periodic one without real-time monitoring the species. In addition, the stability and attractiveness of the periodic orbit are obtained by geometry approach, which ensures a certain robustness of control, i.e., even though the species densities are detected inaccurately or with a deviation, the system will be eventually stable at the periodic orbit under the control action. Furthermore, to obtain the optimum chemical control strength and yield releases of the predator, an optimization problem is constructed. The analytical results presented in the work are validated by numerical simulations for a specific model.