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Niu, Ben; Jiang, Weihua

Multiple scales for two-parameter bifurcations in a neutral equation. (English) Zbl 1267.34127

Nonlinear Dyn. 70, No. 1, 43-54 (2012).
Summary: Van der Pol’s equation with extended delay feedback is investigated as a neutral differential-difference equation. Normal forms near codimension two bifurcations, including Hopf-pitchfork and Hopf-Hopf bifurcation, are determined by the method of multiple scales. Through analyzing the associated amplitude equations, we obtain the detailed bifurcation sets and find some interesting phenomena such as quasi-periodic oscillations and strange attractor, which are confirmed by several numerical simulations.

Cited in 5 Documents

MSC:

34K18 Bifurcation theory of functional-differential equations
34K40 Neutral functional-differential equations
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
34K20 Stability theory of functional-differential equations

Keywords:

multiple scales; neutral differential-difference equation; codimension two bifurcation; van der Pol’s equation; quasi-periodic solution; strange attractor
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References:

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