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1:3 Resonant Double Hopf Bifurcation on Two Coupled Limit Cycle Oscillators with Delay Coupling

WANG Wan-yong1;XU Jian1(1.School of Aerospace Engineering and Applied Mechanics;Tongji University;Shanghai 200092;China)

  The dynamical behaviour of two coupled limit cycle oscillators around a 1:3 resonant double Hopf bifurcation point is analyzed.Three parameters including time delay are chosen as the bifurcation parameters,then the method of multiple scales is used to obtain bifurcation equations.By analyzing the bifurcation equations,the dynamical behaviour arising from the bifurcation is classified qualitatively in two-parameter cross-section by fixing one of the three bifurcation parameters.The results show rich dynamical phenomena including the amplitude death,periodic solution and quasiperiodic solution.In particular,by varying time delay,the exchange of energy between two oscillators is observed.Numerical simulation results are also given to support the theoretical predictions.……