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| Paper IPM / M / 2326 |
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| Abstract: | |||||
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This paper focuses on the qualitative and quantitative analysis of
a generalized three-species food-chain model. The conditions for
the existence and stability of the boundary and positive
equilibria of the model are established. By constructing an
appropriate "bifurcation function", it is shown that the model
undergoes a Hopf bifurcation from the positive equilibrium for
certain parameter values. The root of this bifurcation function
gives the bifurcation value. A robust non-standard numerical
method is constructed and used to obtain the solution of the
model. Numerical simulations using this method show that the Hopf
bifurcation is supercritical with a stable limit cycle in the
positive octant.
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