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• W3039753657 endingPage "2050101" @default.
• W3039753657 startingPage "2050101" @default.
• W3039753657 abstract "Coupled systems of two canonical-dissipative limit cycle oscillators are considered in the general case and for the case of monofrequency and multifrequency synchronization. Specifically, the oscillator frequency ratios of 1:1, 1:2, and 1:3 are examined and modeled by a hybrid Rayleigh–van der Pol oscillator and an oscillator model suggested by Holt as well as an oscillator model suggested by Fokas and Lagerstrom. It is shown that all three systems exhibit a unique bifurcation diagram that describes limit cycle attractors of monofrequency and multifrequency synchronization. In particular, the relative phase describing the lag between the two oscillators both in the monofrequency and multifrequency case can be tuned by an appropriately defined bifurcation parameter [Formula: see text]. For [Formula: see text] two limit cycle attractors with different relative phases exist that merge at [Formula: see text] into pitchfork bifurcations and give rise to single limit cycle attractors that continue to exist for [Formula: see text]. Similarities and differences to bifurcation diagrams published in previous work of a similar coupled oscillator system, one based on Smorodinsky–Winternitz potentials and exhibiting 1:1 synchronization, are noted." @default.
• W3039753657 created "2020-07-10" @default.
• W3039753657 creator A5022221331 @default.
• W3039753657 creator A5023981151 @default.
• W3039753657 date "2020-06-15" @default.
• W3039753657 modified "2023-09-27" @default.
• W3039753657 title "Amplitude Equations and Bifurcation Diagrams for Multifrequency Synchronization of Canonical-Dissipative Oscillators" @default.
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• W3039753657 doi "https://doi.org/10.1142/s0218127420501011" @default.
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