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Global stability of predator-prey system with alternative prey.

Sahoo B - ISRN Biotechnol (2012)

Bottom Line: A predator-prey model in presence of alternative prey is proposed.Global stability conditions for interior equilibrium points are also found.Bifurcation analysis is done with respect to predator's searching rate and handling time.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Daharpur A.P.K.B Vidyabhaban, Paschim Medinipur, West Bengal, India.

ABSTRACT
A predator-prey model in presence of alternative prey is proposed. Existence and local stability conditions for interior equilibrium points are derived. Global stability conditions for interior equilibrium points are also found. Bifurcation analysis is done with respect to predator's searching rate and handling time. Bifurcation analysis confirms the existence of global stability in presence of alternative prey.

No MeSH data available.


Related in: MedlinePlus

Bifurcation diagram of the system with respect to handling time h with fixed searching rate c = 0.5 and for k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, ϵ = 0.4, and d = 0.025. It depicts periodic and stable dynamics.
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fig6: Bifurcation diagram of the system with respect to handling time h with fixed searching rate c = 0.5 and for k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, ϵ = 0.4, and d = 0.025. It depicts periodic and stable dynamics.

Mentions: Bifurcation analysis with respect to handling time h for fixed searching rate c = 0.5, is shown in Figure 6. From Figure 6, I observe that prey population extinct for low values of handling time h but for high values of handling time h the system (2) settles down to steady state. Alternative prey and predator population have no extinction risk, they survive in the system always. For higher searching rate at c = 0.8, the Figure 7 shows that the prey population extinction risk increases for higher values of handling time h. Therefore, the increase of searching rate c shows prey's extinction from the system for higher values of handling time compare to low searching rate.


Global stability of predator-prey system with alternative prey.

Sahoo B - ISRN Biotechnol (2012)

Bifurcation diagram of the system with respect to handling time h with fixed searching rate c = 0.5 and for k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, ϵ = 0.4, and d = 0.025. It depicts periodic and stable dynamics.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4403593&req=5

fig6: Bifurcation diagram of the system with respect to handling time h with fixed searching rate c = 0.5 and for k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, ϵ = 0.4, and d = 0.025. It depicts periodic and stable dynamics.
Mentions: Bifurcation analysis with respect to handling time h for fixed searching rate c = 0.5, is shown in Figure 6. From Figure 6, I observe that prey population extinct for low values of handling time h but for high values of handling time h the system (2) settles down to steady state. Alternative prey and predator population have no extinction risk, they survive in the system always. For higher searching rate at c = 0.8, the Figure 7 shows that the prey population extinction risk increases for higher values of handling time h. Therefore, the increase of searching rate c shows prey's extinction from the system for higher values of handling time compare to low searching rate.

Bottom Line: A predator-prey model in presence of alternative prey is proposed.Global stability conditions for interior equilibrium points are also found.Bifurcation analysis is done with respect to predator's searching rate and handling time.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Daharpur A.P.K.B Vidyabhaban, Paschim Medinipur, West Bengal, India.

ABSTRACT
A predator-prey model in presence of alternative prey is proposed. Existence and local stability conditions for interior equilibrium points are derived. Global stability conditions for interior equilibrium points are also found. Bifurcation analysis is done with respect to predator's searching rate and handling time. Bifurcation analysis confirms the existence of global stability in presence of alternative prey.

No MeSH data available.


Related in: MedlinePlus