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Dynamics of a predator-prey ecological system with nonlinear harvesting rate. (English) Zbl 1340.34169

Summary: A predator-prey ecological system with nonlinear harvesting rate is formulated and studied. This system is described by a differential-algebraic equation. By employing a local parameterization, an equivalent differential system with parameter is obtained. Then by normal form theory and bifurcation theory, the complex dynamics of the system is investigated, including the local stability of the equilibrium point and Hopf bifurcation. Finally, a MATLAB simulation illustrates our results.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34A09 Implicit ordinary differential equations, differential-algebraic equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34C23 Bifurcation theory for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
92D40 Ecology

Software:

Matlab
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Full Text: DOI

References:

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