This paper mainly explores the self-reproducing dynamics in discrete-time system by constructing a two-dimension map with infinitely many fixed points. Theoretical analysis shows that the attractor of the map can not only be non-destructively reproduced by the initial values of all state variables along all axis directions, but can also be non-destructively reproduced by the parameter along all axis directions. The numerical simulations of bifurcation diagram, Lyapunov exponent, phase portrait and iterative sequence are carried out to further confirm the theoretical results. The self-reproducing behavior of different type of attractors and the corresponding iterative sequences are also confirmed by the experimental measurements performed on the DSP-based platform. This map is especially suitable for chaos-based engineering applications since the offset can be periodically switched by the initial condition and parameter on the premise of keeping robust dynamical behavior.

本文主要通过构造具有无限多个不动点的二维映射来探索离散时间系统中的自复制动力学。理论分析表明，该图的吸引子不仅可以由所有状态变量沿所有轴方向的初始值无损再现，而且还可以由参数沿所有轴方向无损再现。对分岔图、李雅普诺夫指数、相图和迭代序列进行了数值模拟，进一步验证了理论结果。在基于 DSP 的平台上进行的实验测量也证实了不同类型吸引子的自复制行为和相应的迭代序列。