论文标题
较高的尺寸极限循环和耦合在动力学系统中诱导的同步
Higher Dimensional Limit Cycles and Coupling Induced Synchronization in Dynamical Systems
论文作者
论文摘要
已广泛研究了极限周期（耗散动力学系统中相邻周期性轨道的吸引子），但是很少讨论过准周期轨道的相应概括。在这里，我们通过分析一对耦合的非相同的van der振荡器和Kuznetsov振荡器来研究“更高维极限循环”。我们发现，Chen，Goldenfeld和Oono引入的基于重新归一化的方法非常适合分析极限周期的准周期类似物。我们还解决了一对强制和耦合的范德波尔振荡器中的夹带问题。我们的原则发现，如果两个这样的独立振荡器一个具有频率夹带而没有频率的独立振荡器，则是线性耦合的，那么可以通过耦合产生夹带的状态。
Limit cycles (attractors for neighbouring periodic orbits in a dissipative dynamical system) have been widely studied but the corresponding generalization for quasi periodic orbits have rarely been discussed. Here we investigate "higher dimensional limit cycles" by analysing a pair of coupled non identical Van der Pol oscillators and also the Kuznetsov oscillator. We find that the renormalization group based approach introduced by Chen, Goldenfeld and Oono is ideally suited for analysing the quasi periodic analogues of limit cycles. We also address entrainment issues in a pair of forced and coupled Van der Pol oscillators. Our principle finding there is that if two such independent oscillators one with frequency entrainment and the other without are coupled linearly, then it is possible to produce an entrained state via the coupling.
