Li, C.; Li, Z.; Jiang, Y.; Lei, T.; Wang, X. Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry. Symmetry2023, 15, 1564.
Li, C.; Li, Z.; Jiang, Y.; Lei, T.; Wang, X. Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry. Symmetry 2023, 15, 1564.
Li, C.; Li, Z.; Jiang, Y.; Lei, T.; Wang, X. Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry. Symmetry2023, 15, 1564.
Li, C.; Li, Z.; Jiang, Y.; Lei, T.; Wang, X. Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry. Symmetry 2023, 15, 1564.
Abstract
A comprehensive review on symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics and even when the symmetry is broken, symmetric pairs of coexisting attractors are born annotating the symmetry in another way. The polarity balance can be recovered by the combinations of the polarity reverse of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reverse from their functions. In this case, conditional symmetry is constructed giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reverse of some of the system variables, which brings more alternatives of chaotic signal and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic system and those of conditional symmetry provide sufficient system options for chao-based applications.
Keywords
symmetry; conditional symmetry; offset boosting; chaotic system
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
