弱耦合映射系统在周期窗口内的行为

BEHAVIOR OF A WEAK COUPLED MAP SYSTEM IN THE PERIODIC WINDOWS

通过解析讨论及数值计算的验证,发现弱耦合映射系统的周期窗口只存在于耦合强度极小的范围内(对于3周期窗口大约为10^(-3)),这个范围可以定义为周期窗口的深度。在周期窗口内耦合映射的行为可以通过讨论少数几个模(相对简单的耦合三映射,实质是一维映射)而确定。耦合映射的第一Lyapunov指数随耦合强度增大的变化曲线呈锯齿形状。

It is shown analytically as well as numerically that a periodic window of the coupled map system exists only for very weak coupling strength (about 10-3 for period 3 window, for instance), which could be defined as the depth of the window. Within the windows the behavior of the coupled map system could be recovered by dealing with a few number of modes, which consist of coupled three maps. The first Lyapunov exponent for the coupled map system shows a 'zigzag' curve form virsus the coupling strength.