Title of article :
Dynamic Hopf bifurcations generated by nonlinear terms
Author/Authors :
D. Rachinskii، نويسنده , , K. Schneider، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2005
Pages :
22
From page :
65
To page :
86
Abstract :
We consider the so-called delayed loss of stability phenomenon for singularly perturbed systems of differential equations in case that the associated autonomous system with a scalar parameter undergoes the Hopf bifurcation at the zero equilibrium point. It is assumed that the linearization of the associated system is independent of the parameter and the next terms in the expansion of the right-hand parts at zero are positive homogeneous of order α>1. Simple formulas are presented to estimate the asymptotic delay for the delayed loss of stability phenomenon. More precisely, we suggest sufficient conditions which ensure that zeros of a simple function ψ defined by the positive homogeneous nonlinear terms are the Hopf bifurcation points of the associated system, the sign of ψ at other points determines stability of the zero equilibrium, and the asymptotic delay equals the distance between the bifurcation point and a zero of some primitive of ψ.
Keywords :
Singular Perturbation , Degenerate linear part , Hopf bifurcation , Delayedloss of stability
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS
Serial Year :
2005
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS
Record number :
750594
Link To Document :
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