The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number. A nonlinear dynamical system drive
n by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor. For Keplers golden stars, we present evidence of the first observation of strange nonchaotic dynamics in nature outside the laboratory. This discovery could aid the classification and detailed modeling of variable stars.
We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the population falls be
low a threshold value. We investigate the global stability of this large interactive system, as indicated by the average number of nodal populations that manage to remain active. Our central result is that the probability of obtaining active nodes in this network is significantly enhanced under fluctuations. Further, we find a sharp transition in the number of active nodes as noise strength is varied, along with clearly evident scaling behaviour near the critical noise strength. Lastly, we also observe noise induced temporal coherence in the active sub-network, namely, there is an enhancement in synchrony among the nodes at an intermediate noise strength.
We study the dynamics of a collection of nonlinearly coupled limit cycle oscillators, relevant to systems ranging from neuronal populations to electrical circuits, under coupling topologies varying from a regular ring to a random network. We find tha
t the trajectories of this system escape to infinity under regular coupling, for sufficiently strong coupling strengths. However, when some fraction of the regular connections are dynamically randomized, the unbounded growth is suppressed and the system always remains bounded. Further we determine the critical fraction of random links necessary for successful prevention of explosive behaviour, for different network rewiring time-scales. These results suggest a mechanism by which blow-ups may be controlled in extended oscillator systems.
