Regional Structure of Two- and Three-Frequency Regimes in a Model of Four Phase Oscillators

DOI10.1142/S0218127422300087zbMath1494.34116OpenAlexW4220994159MaRDI QIDQ5064625

Alexander P. Kuznetsov, Ludmila V. Turukina, Igor R. Sataev

Publication date: 16 March 2022

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127422300087

zbMATH Keywords

bifurcationsynchronizationquasi-periodic oscillationcoupled phase oscillators

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Synchronization of solutions to ordinary differential equations (34D06) Multifrequency systems of ordinary differential equations (34C46)

Cites Work

• Unnamed Item
• Unnamed Item
• About Landau-Hopf scenario in a system of coupled self-oscillators
• Hidden attractors in dynamical systems
• On the road towards multidimensional tori
• Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
• Synchronization. From simple to complex
• Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance `bubble'
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Rotation sets and phase-locking in an electronic three oscillator system
• Synchronization and multi-frequency oscillations in the low-dimensional chain of the self-oscillators
• Theory of hidden oscillations and stability of control systems
• A structure of the oscillation frequencies parameter space for the system of dissipatively coupled oscillators
• Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems
• Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
• The Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms: The Arnol'd resonance web
• BIFURCATION OF QUASI-PERIODIC OSCILLATIONS IN MUTUALLY COUPLED HARD-TYPE OSCILLATORS: DEMONSTRATION OF UNSTABLE QUASI-PERIODIC ORBITS
• Three identical oscillators with symmetric coupling
• Routes to chaos in the Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms
• Three-dimensional tori and Arnold tongues
• LOCAL BIFURCATIONS OF A QUASIPERIODIC ORBIT

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