caa a22 4500 445362065 CHVBK 20180317142918.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s11071-010-9909-x doi (NATIONALLICENCE)springer-10.1007/s11071-010-9909-x Multiple scales analysis for double Hopf bifurcation with1:3resonance [Elektronische Daten] [Wanyong Wang, Jian Xu] The dynamical behavior of a general n-dimensional delay differential equation (DDE) around a 1:3 resonant double Hopf bifurcation point is analyzed. The method of multiple scales is used to obtain complex bifurcation equations. By expressing complex amplitudes in a mixed polar-Cartesian representation, the complex bifurcation equations are again obtained in real form. As an illustration, a system of two coupled van der Pol oscillators is considered and a set of parameter values for which a 1:3 resonant double Hopf bifurcation occurs is established. The dynamical behavior around the resonant double Hopf bifurcation point is analyzed in terms of three control parameters. The validity of analytical results is shown by their consistency with numerical simulations. Springer Science+Business Media B.V., 2010 Multiple scales nationallicence Resonance nationallicence Double Hopf bifurcation nationallicence Time delay nationallicence Wang Wanyong School of Aerospace Engineering and Applied Mechanics, Tongji University, 200092, Shanghai, P.R. China aut Xu Jian School of Aerospace Engineering and Applied Mechanics, Tongji University, 200092, Shanghai, P.R. China aut Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 39-51 0924-090X 66:1-2<39 2011 66 11071 https://doi.org/10.1007/s11071-010-9909-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9909-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Wanyong School of Aerospace Engineering and Applied Mechanics, Tongji University, 200092, Shanghai, P.R. China aut NATIONALLICENCE 700 1- Xu Jian School of Aerospace Engineering and Applied Mechanics, Tongji University, 200092, Shanghai, P.R. China aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/1-2(2011-10-01), 39-51 0924-090X 66:1-2<39 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer