Martí A C, Masoller C
Instituto de Física, Facultad de Ciencias, Universidad de la Republica, Iguá 4225, 11400 Montevideo, Uruguay.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 May;67(5 Pt 2):056219. doi: 10.1103/PhysRevE.67.056219. Epub 2003 May 27.
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized states in which the elements of the array evolve along a periodic orbit of the uncoupled map, while the spatial correlation along the array is such that an individual map sees all other maps in his present, current, state. For values of the nonlinear parameter such that the uncoupled maps are chaotic, time-delayed mutual coupling suppresses the chaotic behavior by stabilizing a periodic orbit that is unstable for the uncoupled maps. The stability analysis of the synchronized state allows us to calculate the range of the coupling strength in which global synchronization can be obtained.
我们研究全局耦合的相同逻辑斯谛映射线性阵列的同步。我们考虑一种时滞耦合，它考虑了相互作用传播的有限速度。我们发现了全局同步状态，其中阵列的元素沿着未耦合映射的周期轨道演化，而沿阵列的空间相关性使得单个映射在其当前状态下能看到所有其他映射。对于非线性参数的值，使得未耦合映射是混沌的，时滞相互耦合通过稳定一个对于未耦合映射不稳定的周期轨道来抑制混沌行为。同步状态的稳定性分析使我们能够计算可获得全局同步的耦合强度范围。
