Department of Physics, Faculty of Science, The University of Ngaoundéré, P.O. Box 454 Ngaoundéré, Cameroon.
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
Phys Rev E. 2017 Dec;96(6-1):062203. doi: 10.1103/PhysRevE.96.062203. Epub 2017 Dec 11.
We investigate the dynamics of coupled identical chaotic Lorenz oscillators just above the subcritical Hopf bifurcation. In the absence of coupling, the motion is on a strange chaotic attractor and the fixed points of the system are all unstable. With the coupling, the unstable fixed points are converted into chaotic attractors, and the system can exhibit a multiplicity of coexisting attractors. Depending on the strength of the coupling, the motion of the individual oscillators can be synchronized (both in and out of phase) or desynchronized and in addition there can be mixed phases. We find that the basins have a complex structure: the state that is asymptotically reached shows extreme sensitivity to initial conditions. The basins of attraction of these different states are characterized using a variety of measures and depending on the strength of the coupling, they are intermingled or quasiriddled.
我们研究了在亚临界 Hopf 分岔以上的耦合相同混沌 Lorenz 振荡器的动力学。在没有耦合的情况下，运动是在一个奇怪的混沌吸引子上，系统的平衡点都是不稳定的。随着耦合的增加，不稳定的平衡点被转化为混沌吸引子，系统可以表现出多种共存的吸引子。根据耦合的强度，个体振荡器的运动可以被同步（同相或反相）或去同步，此外还可能存在混合相。我们发现，吸引盆地具有复杂的结构：渐近达到的状态对初始条件表现出极端的敏感性。使用各种测量方法来描述这些不同状态的吸引盆地，并且取决于耦合的强度，它们是交织的或准条纹的。
