Abstract
Abstract Prey switching strategy is adopted by a predator when they are provided with more than one prey and predator prefers to consume one prey over others. Though switching may occur due to various reasons such as scarcity of preferable prey or risk in hunting the abundant prey. In this work, we have proposed a prey-predator system with a particular type of switching functional response where a predator feeds on two types of prey but it switches from one prey to another when a particular prey population becomes lower. The ratio of consumption becomes significantly higher in the presence of prey switching for an increasing ratio of prey population which satisfies Murdoch’s condition [15]. The analysis reveals that two prey species can coexist as a stable state in absence of predator but a single prey-predator situation cannot be a steady state. Moreover, all the population can coexist only under certain restrictions. We get bistability for a certain range of predation rate for first prey population. Moreover, varying the mortality rate of the predator, an oscillating system can be obtained through Hopf bifurcation. Also, the predation rate for the first prey can turn a steady-state into an oscillating system. Except for Hopf bifurcation, some other local bifurcations also have been studied here. The figures in the numerical simulation have depicted that, if there is a lesser number of one prey present in a system, then with time, switching to the other prey, in fact, increases the predator population significantly.
Highlights
For two-prey and one-predator system, the growth rate of a predator population depends on the total amount of consumed prey and on the ratio of the captured prey species
We have proposed a prey-predator system with a particular type of switching functional response where a predator feeds on two types of prey but it switches from one prey to another when a particular prey population becomes lower
Prey switching mainly describes a situation when predator prefers a particular prey over others due to their abundance and availability in the environment, i.e., in some cases, there exists a strong preference for those prey which can be found and a weak preference for those prey which are available in a smaller quantity
Summary
For two-prey and one-predator system, the growth rate of a predator population depends on the total amount of consumed prey and on the ratio of the captured prey species. ; where x , x respectively be the biomass of rst and second prey population which are consumed at rates h , h by the predator. The parameters η and η represent the consumption rate coe cients of the predator on rst and second prey species respectively. The interior equilibrium point E* of system (2.2) undergoes cusp bifurcation at the threshold (r , γ ) = (r [CP], γ [CP]) around E*(x* , x* , y*) when G(x ) = in equation (5.1) has a triple root in Ω. If the predator mortality rate starts to decrease, below a certain value (d[TC]) the trajectory approaches towards interior equilibrium point E* instead of E. Gure (6.b) and (7.b) depict an oscillating behaviour of the system and occurrence of a stable limit cycle around unstable equilibrium
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