【摘 要】
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In this paper, a semi-analytical procedure for studying stability and bifurcations of limit cycles in higher-dimensional nonlinear autonomous dynamical systems is developed.This procedure is based mai
【机 构】
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School of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350007,China
【出 处】
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The Third International Conference on Dynamics,Vibration and
论文部分内容阅读
In this paper, a semi-analytical procedure for studying stability and bifurcations of limit cycles in higher-dimensional nonlinear autonomous dynamical systems is developed.This procedure is based mainly on the incremental harmonic balance (IHB) method.It is composed of three key steps, namely, the determination of limit cycles by 1HB method, the calculation of transition matrix by precise integration (PI) algorithm and the discrimination of limit cycle stability by Floquet theory.As an application, the procedure is used to investigate the dynamics of the limit cycle of a three-dimensional nonlinear autonomous dynamical system.The symmetry-breaking bifurcation, the first and the second period-doubling bifurcations of the limit cycle are identified.The critical parameter values corresponding to these bifurcations are calculated.The phase portraits and bifurcation points agree well with those of direct numerical integrations by using Runge-Kutta method.
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