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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

The trajectory and time series diagrams of prey, alternative prey, and predator population of the system for k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, c = 0.6, h = 0.5, ϵ = 0.4, and d = 0.025.
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fig2: The trajectory and time series diagrams of prey, alternative prey, and predator population of the system for k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, c = 0.6, h = 0.5, ϵ = 0.4, and d = 0.025.

Mentions: I choose the parameters as k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, c = 0.6, h = 0.5, ϵ = 0.4, and d = 0.025. Then it follows from the Theorem 3 that the unique positive interior equilibrium point E*(x*, y*, z*) = (0.079135,2.2566,3.34253) is globally stable which is shown in Figure 2.


Global stability of predator-prey system with alternative prey.

Sahoo B - ISRN Biotechnol (2012)

The trajectory and time series diagrams of prey, alternative prey, and predator population of the system for k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, c = 0.6, h = 0.5, ϵ = 0.4, and d = 0.025.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig2: The trajectory and time series diagrams of prey, alternative prey, and predator population of the system for k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, c = 0.6, h = 0.5, ϵ = 0.4, and d = 0.025.
Mentions: I choose the parameters as k1 = 3.0, k2 = 2.5, p = 0.5, q = 0.05, a = 0.5, c = 0.6, h = 0.5, ϵ = 0.4, and d = 0.025. Then it follows from the Theorem 3 that the unique positive interior equilibrium point E*(x*, y*, z*) = (0.079135,2.2566,3.34253) is globally stable which is shown in Figure 2.

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