About the chaos influence on a system with multi-frequency quasi-periodicity and the Landau-Hopf scenario

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED Physica D: Nonlinear Phenomena Pub Date : 2024-11-06 DOI:10.1016/j.physd.2024.134425

A.P. Kuznetsov, L.V. Turukina

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Abstract

The interaction of system demonstrating multi-frequency quasi-periodic oscillations and several steps of the Landau-Hopf scenario with chaotic Rössler system is considered. The quasi-periodic subsystem is a network of five non-identical van der Pol oscillators. It is shown that as the coupling parameter between the subsystems decreases, successive quasi-periodic Hopf bifurcations and doublings of high-dimensional invariant tori are observed. The chaos arising in this system can have several (in our case up to five) additional zero Lyapunov exponents. In case of weak coupling parameter between chaotic and quasi-periodic subsystems, when the coupling parameter of van der Pol oscillators changes, the points at which the attractor transformation occurs are observed. This is a new type of bifurcations that are responsible for a consistent increase in the number of additional zero Lyapunov exponents. As the coupling parameter between chaotic and quasi-periodic subsystems increases, the observed stages of the Landau-Hopf scenario turns out to be resistant to interaction with the chaotic system.

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关于混沌对多频准周期性系统的影响以及 Landau-Hopf 情景

研究考虑了显示多频率准周期振荡和兰道-霍普夫情景几个步骤的系统与混沌罗斯勒系统的相互作用。准周期子系统是由五个非同范德尔波尔振荡器组成的网络。研究表明，随着子系统之间耦合参数的减小，会观察到连续的准周期霍普夫分岔和高维不变环的加倍。在这个系统中产生的混沌可能有几个（在我们的例子中最多有五个）额外的零 Lyapunov 指数。在混沌子系统和准周期子系统之间存在弱耦合参数的情况下，当范德尔波尔振荡器的耦合参数发生变化时，就会观察到吸引子转换发生的点。这是一种新型分岔，是额外零 Lyapunov 指数数量持续增加的原因。随着混沌子系统和准周期子系统之间耦合参数的增加，观察到的朗道-霍普夫情景阶段原来可以抵抗与混沌系统的相互作用。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.