DYNAMICS OF A LIMIT CYCLE OSCILLATOR WITH EXTENDED DELAY FEEDBACK

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.