|
Time-delay systems are very common in real life problems. In fact the reaction of real world systems is never instantaneous and it always needs some time to travel. We will discuss a general bifurcation in such nonlinear oscillators [1,2,3] when their interaction is time--delayed. As the delay parameter is varied, the relative phase between the oscillators changes abruptly from zero to π or vice versa.
We will also discuss the phenomenon of anomalous phase synchronization where the degree of disorder in the oscillator frequencies, as characterized by their variance, first increases with coupling before eventually decreasing. We show that this effect can be enhanced [4] when a time delay is included in the coupling.
We will also introduce a type of integral coupling which is due to the response-time of the interacting subsystems. The results for combined effect of time-delay and integral coupling will be presented.
[1] A. Prasad, Phys. Rev. E, 72, 056204,(2005). [2] A. Prasad, J. Kurths, S. K. Dana and R. Ramaswamy, Phys. Rev. E, 74, 035204(R)(2006). [3] A. Prasad, S. K. Dana, R. Karnatak, J. Kurths, B. Blasius, and R. Ramaswamy, CHAOS 18, 023111 (2008). [4] A. Prasad, J. Kurths and R. Ramaswamy, Physics Letters A 372, 6150 (2008). |
|