Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-IV Functional Response
Tóm tắt
In this paper the dynamical behaviors of a predator-prey
system with Holling Type-IV functional response are investigated
in detail by using the analyses of qualitative method,
bifurcation theory, and numerical simulation. The qualitative
analyses and numerical simulation for the model indicate that it
has a unique stable limit cycle. The bifurcation analyses of the
system exhibit static and dynamical bifurcations including
saddlenode bifurcation, Hopf bifurcation, homoclinic bifurcation
and bifurcation of cusp-type with codimension two (ie, the
Bogdanov-Takens bifurcation), and we show the existence of
codimension three degenerated equilibrium and the existence of
homoclinic orbit by using numerical simulation.
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