2020/02/12 by Ryan Roopnarain, Roopnarain, Ryan, Subhagata Choudhury +1
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation #Chaos control and synchronization
paper · pdf · doi:10.48550/arxiv.2002.05278
The effects of a distributed 'weak generic kernel' delay on cyclically\ncoupled limit cycle and chaotic oscillators are considered. For coupled Van der\nPol oscillators (and in fact, other oscillators as well) the delay can produce\ntransitions from amplitude death(AD) or oscillation death (OD) to Hopf\nbifurcation-induced periodic behavior, with the delayed limit cycle shrinking\nor growing as the delay is varied towards or away from the bifurcation point\nrespectively. The transition from AD to OD is mediated here via a pitchfork\nbifurcation, as seen earlier for other couplings as well. Also, the cyclically\ncoupled undelayed van der Pol system here is already in a state of AD/OD, and\nintroducing the delay allows both oscillations and AD/OD as the delay parameter\nis varied. This is in contrast to other limit cycle systems, where diffusive\ncoupling alone does not result in the onset of AD/OD. For systems where the\nindividual oscillators are chaotic, such as a Sprott oscillator system or a\ncoupled van der Pol-Rayleigh system with parametric forcing, the delay may\nproduce AD/OD (as in the Sprott case), with the AD to OD transition now\noccurring via a transcritical bifurcation instead. However, this may not be\npossible, and the delay might just vary the attractor shape. In either of these\nsituations however, increased delay strength tends to cause the system to have\nsimpler behavior, streamlining the shape of the attractor, or shrinking it in\ncases with oscillations.\n