论文标题
耗散性超基因中不变的托里
Invariant tori in dissipative hyperchaos
论文作者
论文摘要
了解非线性耗散系统混乱动力学的一种方法是研究嵌入该系统混沌吸引子中的非差异但动态不稳定的不稳定溶液。零维的不稳定固定点和一维不稳定的周期轨道捕获时间周期动力学的一维周期轨道被广泛接受，包括流体湍流在内，而较高维度不变性的圆环则很少被认为是Quasi-Periotic动力学的。我们证明，不稳定的2氧气通常嵌入了普通微分方程的耗散系统的过度降低吸引子中；可以通过不稳定周期轨道的分叉来识别托里，并且它们的参数延续和稳定性特性的表征是可行的。由于预期较高维的托里在结构上是不稳定的，因此2-tori以及周期性的轨道和平衡形成了一组完整的相关不变解决方案，以基于混乱的动态描述。
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional unstable fixed points and one-dimensional unstable periodic orbits capturing time-periodic dynamics is widely accepted for high-dimensional chaotic systems including fluid turbulence, while higher-dimensional invariant tori representing quasi-periodic dynamics have rarely been considered. We demonstrate that unstable 2-tori are generically embedded in the hyperchaotic attractor of a dissipative system of ordinary differential equations; that tori can be numerically identified via bifurcations of unstable periodic orbits and that their parametric continuation and characterization of stability properties is feasible. As higher-dimensional tori are expected to be structurally unstable, 2-tori together with periodic orbits and equilibria form a complete set of relevant invariant solutions on which to base a dynamical description of chaos.
