DYNAMICS OF A LIMIT CYCLE OSCILLATOR WITH EXTENDED DELAY FEEDBACK

作者：Niu, Ben; Jiang, Weihua^*

来源：Discrete and Continuous Dynamical Systems-Series B, 2013, 18(5): 1439-1458.

DOI：10.3934/dcdsb.2013.18.1439

• Extended delay feedback
• limit cycle oscillator
• neutral type
• double Hopf bifurcation
• quasiperiodic solution

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.

• 出版日期2013-7
• 单位哈尔滨学院; 哈尔滨工业大学