Abstract
We investigate the dynamical behaviors of two-prey one-predator model with general Holling type functional responses. The effect of seasonal perturbation on the model has been discussed analytically as well as numerically. The periodic fluctuation is considered in prey growth rate and the predator mortality rate of the model. The impulsive effects involving biological and chemical control strategy, periodic releasing of natural enemies, and spraying pesticide at different fixed times are introduced in the model with seasonal perturbation. We derive the conditions of stability for impulsive system using Floquet theory, small amplitude perturbation skills. A local asymptotically stable prey (pest) eradicated periodic solution is obtained when the impulsive period is less than some critical value. Numerical simulations of the model with and without seasonal disturbances exhibit different dynamics. Also we simulate numerically the model involving seasonal perturbations without impulse and with impulse. Finally, concluding remarks are given.
Highlights
Functional response plays an important role in dynamics of population ecology
We investigate the dynamical behaviors of two-prey one-predator model with general Holling type functional responses
In contrast to the linear increase of type I, type II approaches saturation gradually at higher prey density. This behavior is better expressed by an asymptotic relationship between per capita feeding rate and prey density which is of the functional form mN/(1 + ̂bN), where N is the prey density. m andb are positive constants describing the effects of capture rate and handling time on the feeding rate of the predator, respectively
Summary
Functional response plays an important role in dynamics of population ecology. There are several examples in nature where the predator population affects the number of their prey populations. In this paper we investigate how two-prey one-predator model with general Holling type functional responses changes its dynamics with change in seasonal parameters like degree of seasonality. Pei et al [20] have considered two prey and one predator with group defense and Holling type II functional responses and investigated the effect of impulsive perturbation in pest control using pesticides. We study general Holling type two prey (pests) and one predator with seasonal disturbances as well as proportional periodic impulsive poisoning (spraying pesticide) for all species and constant periodic releasing, or immigrating, for the predator at different fixed time.
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