A seasonally competitive m-prey and n-predator impulsive system modeled by general functional response for integrated pest management

Considering the harvesting of prey and stocking of predator impulsively at different fixed moments of time, this paper studies the dynamics of a seasonally competitive m-prey and n-predator impulsive system, which is focused more specifically in four areas as follows: (i) we emphasize the dynamics of m-prey and n-predator in the ecosystem with a view to understanding how the present work may be able to apply to real environment applications; (ii) this work uses the general functional response instead of using specific impulse responses; (iii) considering the intra- and inter-competitions between species and (iv) the system is subjected to the influences of seasonal factors which imposes direct impacts to the delicate balance of biological systems. By using the comparison techniques and the Floquet theorems, the sufficient conditions for the ecosystem permanence and the asymptotic stabilities of the global and local prey-free periodic solutions have been subsequently obtained. This work is concluded with an in-depth discussion of the biological significance of the results obtained in this research. The obtained results can provide theoretical support for protecting endangered species and to help maintain the ecological balance, especially when it is applied to practical pest management, such as rodent controls in the farmland.