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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 searching rate c with fixed handling time h = 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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fig5: Bifurcation diagram of the system with respect to searching rate c with fixed handling time h = 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: Figure 5 is the bifurcation diagram of the system with respect to searching rate c with fixed handling time h = 0.5. From Figure 5, I observe that prey population has extinction risk for lower values of searching rate c and for higher searching rate it reaches steady state. On the other hand, alternative prey and predator population show periodic behaviour for lower searching rate c and for higher searching rate they go to steady states. Therefore, alternative prey and predator population have no extinction risk; they survive in the system always.


Global stability of predator-prey system with alternative prey.

Sahoo B - ISRN Biotechnol (2012)

Bifurcation diagram of the system with respect to searching rate c with fixed handling time h = 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

Show All Figures
getmorefigures.php?uid=PMC4403593&req=5

fig5: Bifurcation diagram of the system with respect to searching rate c with fixed handling time h = 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: Figure 5 is the bifurcation diagram of the system with respect to searching rate c with fixed handling time h = 0.5. From Figure 5, I observe that prey population has extinction risk for lower values of searching rate c and for higher searching rate it reaches steady state. On the other hand, alternative prey and predator population show periodic behaviour for lower searching rate c and for higher searching rate they go to steady states. Therefore, alternative prey and predator population have no extinction risk; they survive in the system always.

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