论文标题
在高维系统中搜索周期的变异方法减少
A reduced variational approach for searching cycles in high-dimensional systems
论文作者
论文摘要
在具有高维相空间的复杂系统中搜索复发模式是不同领域的重要任务。在当前的工作中，提出了改进的方案，以加速最近设计的变分方法，以根据存在在各种空间扩展系统中广泛观察到的惯性歧管，尤其是那些尺寸较高的系统，以发现具有混乱动力学的系统的周期性轨道。在保持变分方法的指数收敛的前提下，得出有效的循环进化方程以大大减少存储和计算时间。通过反复修改局部坐标并交替进行猜测环的演变，可以有效地实现快速收敛和还原方案的稳定性。局部坐标子空间的尺寸通常大于非负Lyapunov指数的数量，以确保指数收敛。在几个众所周知的示例中成功证明了该提出的方案，并有望在探索高维非线性系统时提供强大的工具。
Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for finding periodic orbits in systems with chaotic dynamics based on the existence of inertial manifold widely observed in various spatially extended systems, especially those with high dimensions. On the premise of keeping exponential convergence of the variational method, an effective loop evolution equation is derived to greatly reduce the storage and computing time. With repeated modification of local coordinates and evolution of the guess loop being carried out alternately, the rapid convergence and the stability of the reduction scheme are effectively achieved. The dimension of local coordinate subspaces is generally larger than the number of nonnegative Lyapunov exponents to ensure the exponential convergence. The proposed scheme is successfully demonstrated on several well-known examples and expected to supply a powerful tool in the exploration of high-dimensional nonlinear systems.
