ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kuznetsov A. P., Turukina L. V. On the interaction of a system with multifrequency oscillations with a chaotic generator. Izvestiya VUZ. Applied Nonlinear Dynamics, 2025, vol. 33, iss. 6, pp. 785-803. DOI: 10.18500/0869-6632-003172, EDN: SUWUZF

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Russian
Heading: 
Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003172
EDN: 
SUWUZF

On the interaction of a system with multifrequency oscillations with a chaotic generator

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Turukina Lyudmila Vladimirovna, Saratov State University
Abstract: 

The purpose of the work: to study the influence of the dynamics of a chaotic system on a system with multi-frequency quasi-periodicity and the Landau-Hopf scenario. The Kislov-Dmitriev chaotic system and an ensemble of van der Pol oscillators with non-identical excitation parameters are chosen as the object of study.

Methods. The analysis was carried out using graphs of Lyapunov exponents and the criterion for identifying types of quasiperiodic bifurcations based on them.

Results. Scenarios of the changing of the regime’s types are presented as the coupling parameter between the subsystems decreased. They may have certain features. Thus, the transition from a three-frequency to a four-frequency regime occurs not through a quasiperiodic Hopf bifurcation, but through a chaos window. The latter is characterized by three or four zero Lyapunov exponents. Inside this chaotic window, a peculiar bifurcation is possible. It is corresponding to an increase in the number of zero Lyapunov exponents according to the type of a saddle-node Hopf bifurcation. Chaos with a different number of zero exponents is observed as the coupling parameter of van der Pol oscillators varied. In this case, a cascade of points corresponding to a step-by-step increase in the number of zero exponents occurs according to a different scenario. It is to a certain extent similar to a quasiperiodic Hopf bifurcation. When the control parameter When the control parameter of the Kislov-Dmitriev system increases, hyperchaos with three zero Lyapunov exponents may appear in the combined system. An inverted order of changing modes is also possible. In this case, for example, a three-frequency regime turns into a four-frequency regime through a chaotic window.

Conclusion. The obtained results expand conception about high-dimensional chaos with several zero Lyapunov exponents and its transformations with parameter changes.
 

Key words: 
chaos
Hyperchaos
quasi-periodicity
Lyapunov exponents
bifurcations
Acknowledgments: 
The work was carried out within the framework of the state assignment of the V. A. Kotelnikov Institute of Radioelectronics (F FW Z − 2025 − 0016), Russian Academy of Sciences, Russia
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Received: 
17.01.2025
Accepted: 
02.04.2025
Available online: 
22.04.2025
Published: 
28.11.2025
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