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<p>What is most fundamental in dynamics of Complex Networks of nonlinear coupled systems (CN) are phenomena connected with different types of their collective behavior. In this article, the author presents the results obtained from applying a novel method—Transversely Directioned Lyapunov Exponents (TDLE) designed for efficient monitoring and controlling CNs. It was shown that the application of TDLEs in a wide range of contexts allows the demonstration of features of CNs that were previously unobservable using other methods. Author proved that application of TDLE allowed observations of new aspects of symmetry breaking. TDLEs have also been proved to be the most effective tool in investigating CNs, as they expose early tendencies of oscillators to synchronize, or split their dynamics, long before the system stabilizes. Another significant benefit of this approach application is connected with the way TDLEs are arrived at, giving possibility to be applied in experiments and control.</p>

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Investigations of complex systems’ dynamics, based on reduced amount of information: part 2—Transversely Directioned Lyapunov Exponents and new aspects of symmetry breaking

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Artur Dabrowski

摘要

What is most fundamental in dynamics of Complex Networks of nonlinear coupled systems (CN) are phenomena connected with different types of their collective behavior. In this article, the author presents the results obtained from applying a novel method—Transversely Directioned Lyapunov Exponents (TDLE) designed for efficient monitoring and controlling CNs. It was shown that the application of TDLEs in a wide range of contexts allows the demonstration of features of CNs that were previously unobservable using other methods. Author proved that application of TDLE allowed observations of new aspects of symmetry breaking. TDLEs have also been proved to be the most effective tool in investigating CNs, as they expose early tendencies of oscillators to synchronize, or split their dynamics, long before the system stabilizes. Another significant benefit of this approach application is connected with the way TDLEs are arrived at, giving possibility to be applied in experiments and control.