论文标题
通过最佳原理找到两个离散动力系统之间轨道的相似性
Finding similarity of orbits between two discrete dynamical systems via optimal principle
论文作者
论文摘要
在物体运动中两个物理过程与行为的复杂性之间是否存在相似性是科学的基本问题。如何通过采用定量和定性研究技术寻求相似性仍然是我们面临的紧迫挑战。为此，介绍了相似性转化矩阵和相似性度的概念，以描述两个似乎无关紧要的复杂离散动力系统之间的轨道相似性。此外，我们提出了一个一般的最佳原理，从动力学系统的角度与优化理论相结合，给出了严格的表征。对于众所周知的混乱动态系统的例子，例如Lorenz吸引子，Chua的电路，R $ \ rm \ rm \ ddot {o} $ ssler吸引子，陈吸引子，l $ \ rm \ rm \ rm \ ddot {u} $吸引者和混合系统，并具有一些富裕的表现，并以某些数字概念的形式证明了一些数字构想，以表现出一些数字的构图，并以此为基础。通过我们提出的最佳原理动力学。
Whether there is similarity between two physical processes in the movement of objects and the complexity of behavior is an essential problem in science. How to seek similarity through the adoption of quantitative and qualitative research techniques still remains an urgent challenge we face. To this end, the concepts of similarity transformation matrix and similarity degree are innovatively introduced to describe similarity of orbits between two complicated discrete dynamical systems that seem to be irrelevant. Furthermore, we present a general optimal principle, giving a strict characterization from the perspective of dynamical systems combined with optimization theory. For well-known examples of chaotic dynamical systems, such as Lorenz attractor, Chua's circuit, R$\rm\ddot{o}$ssler attractor, Chen attractor, L$\rm\ddot{u}$ attractor and hybrid system, with using of the homotopy idea, some numerical simulation results demonstrate that similarity can be found in rich characteristics and complex behaviors of chaotic dynamics via the optimal principle we presented.
