Dynamics of a limit cycle oscillator with extended delay feedback
Ben Niu Weihua Jiang
Discrete & Continuous Dynamical Systems - B 2013, 18(5): 1439-1458 doi: 10.3934/dcdsb.2013.18.1439
Investigating limit cycle oscillator with extended delay feedback is an efficient way to understand the dynamics of a global coupled ensemble or a large system with periodic oscillation. The stability and bifurcation of the arisen neutral equation are obtained. Stability switches and Hopf bifurcations appear when delay passes through a sequence of critical values. Global continuation of Hopf bifurcating periodic solutions and double--Hopf bifurcation are studied. With the help of the unfolding system near double--Hopf bifurcation obtained by using method of normal forms, quasiperiodic oscillations are found. The number of the coexisted periodic solutions is estimated. Finally, some numerical simulations are carried out.
keywords: Extended delay feedback quasiperiodic solution. double Hopf bifurcation limit cycle oscillator neutral type

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