caa a22 4500 445360429 CHVBK 20180317142913.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s11071-010-9852-x doi (NATIONALLICENCE)springer-10.1007/s11071-010-9852-x Dynamics of three coupled limit cycle oscillators withvastlydifferent frequencies [Elektronische Daten] [Hiba Sheheitli, Richard Rand] A system of three coupled limit cycle oscillators with vastly different frequencies is studied. The three oscillators, when uncoupled, have the frequencies ω 1=O(1), ω 2=O(1/ε) and ω 3=O(1/ε 2), respectively, where ε≪1. The method of direct partition of motion (DPM) is extended to study the leading order dynamics of the considered autonomous system. It is shown that the limit cycles of oscillators 1 and 2, to leading order, take the form of a Jacobi elliptic function whose amplitude and frequency are modulated as the strength of coupling is varied. The dynamics of the fastest oscillator, to leading order, is unaffected by the coupling to the slower oscillator. It is also found that when the coupling strength between two of the oscillators is larger than a critical bifurcation value, the limit cycle of the slower oscillator disappears. The obtained analytical results are formal and are checked by comparison to solutions from numerical integration of the system. Springer Science+Business Media B.V., 2010 Coupled oscillators nationallicence DPM nationallicence Method of direct partition of motion nationallicence Bifurcations nationallicence Sheheitli Hiba Dept. Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA aut Rand Richard Dept. Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA aut Nonlinear Dynamics Springer Netherlands 64/1-2(2011-04-01), 131-145 0924-090X 64:1-2<131 2011 64 11071 https://doi.org/10.1007/s11071-010-9852-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9852-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sheheitli Hiba Dept. Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA aut NATIONALLICENCE 700 1- Rand Richard Dept. Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 64/1-2(2011-04-01), 131-145 0924-090X 64:1-2<131 2011 64 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer