Abstract
The paper is concerned with Hopf bifurcations in systems of autonomous ordinary differential equations with a parameter. The principal distinction between usual theorems on Hopf bifurcations and our results is that here the linearized equation is degenerate and independent of the parameter. We present sufficient conditions for a parameter value to be a bifurcation point and analyze properties of ...
Abstract
The paper is concerned with Hopf bifurcations in systems of autonomous ordinary differential equations with a parameter. The principal distinction between usual theorems on Hopf bifurcations and our results is that here the linearized equation is degenerate and independent of the parameter. We present sufficient conditions for a parameter value to be a bifurcation point and analyze properties of small cycles arising in the vicinity of the equilibrium. Sublinear nonlinearities play the main role in the results obtained, (C) 2002 Elsevier Science.
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