Abstract
In this work, our aim is to investigate the impact of a non‐Kolmogorov predator‐prey‐subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have derived sufficient conditions for the existence of local bifurcations of codimension 1 (transcritical and Hopf bifurcation). It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator‐prey‐subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources.
Highlights
In the ecological system, the predator-prey interaction is one of the most significant tools which is comparatively easy to observe in the field
Fear of the predator felt by the prey plays a vital role since its effect is stronger than direct predation [1, 2]. e cost of fear can reduce the reproduction rate of prey because it affects the physiological condition of prey population
Motivated by the works of Das and Samanta [35], Nevai and Van Gorder [28], and Xu et al [36], we have analyzed the dynamical behaviour of a mathematical model of non-Kolmogorov form that includes the three components with the impacts of nonlinear prey refuge function and the fear effect felt by the prey in the presence of the predator
Summary
The predator-prey interaction is one of the most significant tools which is comparatively easy to observe in the field. It has been experimentally investigated that, in the absence of direct killing, the reproduction of the offspring of song sparrows (Melospiza melodia) could be reduced by 40% as a result of impact of feeling fear created by the predator [4] This reduction caused by the antipredator behaviour affects the birth rate and survival of offspring. Motivated by the works of Das and Samanta [35], Nevai and Van Gorder [28], and Xu et al [36], we have analyzed the dynamical behaviour of a mathematical model of non-Kolmogorov form that includes the three components (predator, prey, and subsidy) with the impacts of nonlinear prey refuge function and the fear effect felt by the prey in the presence of the predator.
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