Modeling the Effect of Interference and Gestation Delay in an Interacting Good Biomass and Bird Population: An Application to Wetland Ecosystem

Abstract

This paper analyzes the interacting good bio-mass and bird population for the wetland system of Keoladeo National Park (KNP). The system dynamics is analyzed with and without time delay. The bifurcating periodic solution properties are investigated by normal form and central manifold arguments. The computer simulation is performed to validate the analytical findings that show the different dynamical outcomes such as stable and oscillatory dynamics in the absence of time delay. The numerical computation is performed for the delayed system and the stability behavior of gestation delay for different cases is investigated. The system dynamics show the chaotic behavior when the two crucial parameters (carrying capacity of good biomass and intensity of interference of bird population) have a high time delay value. Further, the diffusion-induced instability conditions are derived. The obtained spatial patterns show that the time and intensity of interference can change the spatial distributions, and the hot and cold spots pattern appears in the whole domain.