切延迟作用下的TD-ERCS混沌系统的周期轨道研究
Studies on Periodic Trajectories of TD-ERCS Chaotic System with Delay Operation m≥1
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摘要: 重点研究了切延迟操作m≥1时系统的周期轨道的存在性问题.通过研究切延迟操作的物理图象,引入反射性等价概念,给出了切延迟操作下周期轨道判据.通过引入过渡态、正常态和正则周期轨道概念,导出了切延迟操作m≥1下可能存在的正则周期轨道,讨论了周期轨道的分布和基本判别方法,特别是短的正则周期轨道,稳定的周期轨道对于TD-ERCS混沌系统的安全性来说是致命的.
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关键词:
- TD-ERCS,混沌,周期轨道,对称性
Abstract: This paper lays its emphasis upon the existence of the periodic trajectories in TD-ERCS under the tangent-delay operation n≥1. A criterion on the periodic trajectories is given under the tangent-delay operation m≥1 by discussing the physical image of tangent-delay operation and defining a conception of reflection equivalence. The existence of regularized periodic trajectories is proved under the tangent-delay operation m≥1 by introducing the transient state and the regular state and defining regularized periodic trajectories, especially, some short regularized periodic trajectories are given. The stability problem will be discussed in the next paper. -
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