Toral Raul, Mirasso Claudio R., Hernandez-Garcia Emilio, Piro Oreste
Instituto Mediterraneo de Estudios Avanzados, IMEDEA, CSIC-UIBDepartament de Fisica, Universitat de les Illes Balears, 07071 Palma de Mallorca, Spain.
Chaos. 2001 Sep;11(3):665-673. doi: 10.1063/1.1386397.
We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of one-dimensional maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon. (c) 2001 American Institute of Physics.
我们研究了注入常见噪声源对混沌系统轨迹的影响，解决了文献中存在的一些相互矛盾的结果。我们给出了处于混沌区域的一维映射和洛伦兹系统的具体例子，并给出了数值证据，表明向从不同初始条件出发的不同轨迹添加共同噪声最终会导致它们完美同步。当同步发生时，最大李雅普诺夫指数变为负数。对于一个简单的映射，我们能够通过分析证明这一现象。最后，我们分析了该现象的结构稳定性。(c) 2001美国物理研究所。
