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Hopf-transcritical bifurcation in retarded functional differential equations
Nonlinear Analysis: Theory, Methods & Applications, 2010Firstly, a codimension-two unfolding for the Hopf-transcritical bifurcation is studied, and complete bifurcation diagrams and phase portraits are given. In particular, the heteroclinic bifurcation curve is investigated explicitly, and conditions are obtained under which the secondary bifurcation periodic solutions and the heteroclinic orbit are stable.
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Homoclinic flip bifurcations accompanied by transcritical bifurcation
Chinese Annals of Mathematics, Series B, 2011The author investigates the bifurcation of a homoclinic loop with a nonhyperbolic equilibrium by constructing a suitable Poincaré map. Using the fundamental solutions to linear variational equations as an active coordinate system, he constructs a global map which is composed of a regular map in the tubular neighborhood of the homoclinic orbit and a ...
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BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION
International Journal of Bifurcation and Chaos, 2008The bifurcations of generic heteroclinic loop with one nonhyperbolic equilibrium p1and one hyperbolic saddle p2are investigated, where p1is assumed to undergo transcritical bifurcation. Firstly, we discuss bifurcations of heteroclinic loop when transcritical bifurcation does not happen, the persistence of heteroclinic loop, the existence of homoclinic ...
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