Stability and bifurcation analysis of a nonlinear dynamical model studying the decline of vulture population

Abstract

A nonlinear dynamical model is developed in this paper that depicts interactions among vultures, human, animals and their carcasses. Diseases such as plague, anthrax and rabies are spreading due to the cascade impact caused by the catastrophic drop in the vulture population, particularly in Africa and Asia. The built model is theoretically studied using qualitative differential-equation theory to demonstrate the system’s rich dynamical features, which are critical for maintaining the ecosystem’s equilibrium. According to the qualitative findings, depending on the parameter combinations, the system not only displays stability of many equilibrium states but also experiences transcritical and Hopf bifurcations. By keeping an eye on the variables causing the decline of the vulture population, the model’s outputs may assist in maintaining balance with the prevention of the spread of disease through carcasses. Hopf-bifurcation results in the bifurcation of the limit cycle through the threshold, supporting the idea that interactions between humans and vultures may also be periodic.