Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting

Abstract

In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

The Impacts of Scavenging on the Prey-Predator-Scavenger Fishery Model in the Existence of Harvesting and Toxin

“…Based on the standard linearisation technique and the Routh-Hurwitz criterion [4,[13][14][15][17][18][19], we derive the local stability conditions for feasible non-coexistence steady-states of the system Eq. (2).…”

“…The coexistence steady-state 𝑃 5 depends on the scavenging parameter 𝜖. Based on the Hopf bifurcation theorem applied in the research conducted by Satar and Naji [4], Gupta and Chandra [13] and Panja [18], it is known that a system Eq. ( 2…”

“…Foraging interaction primarily focuses on prey-predator interaction, whereas the use of carrion by scavengers, as the best form of animal carcasses, has received little attention in the ecosystem sense. Scavengers research, according to Satar and Naji [4], is important because they help clean the environment. However, excessive scavenging activities, especially for facultative scavengers which consumed both live and dead animals can make their population dominant in the fishery ecosystem and eventually both prey and predator fish species are driven to extinction.…”

“…To solve the problem of ecosystem extinction, mathematical models are used to analyse significant parameters, threshold conditions and stability of a variety of ecological systems. In the existence of harvesting and toxic substances, Satar and Naji [4] examined the stability and bifurcation of a preypredator-scavenger model. A bifurcation takes place when a parameter in a population system crosses a threshold value, resulting in an abrupt dynamical change [12].…”

“…According to previous research, there is still a dearth of studies that consider the toxicant and harvesting aspects of the prey-predator-scavenger system. The previous studies that can be reviewed from the papers of several authors in [4,[6][7][8][9][10][11][14][15][16] have motivated us to analyse the impacts of scavenging by facultative scavengers on the dynamics of the prey-predator-scavenger fishery model in the presence of self-produced toxins by fish populations and harvesting. For the preservation and conservation of the fishery ecosystem, we think it will contribute to richer dynamics in the behaviours of the fishery model.…”