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- W2377777621 abstract "A single-degree-of-freedom system with quadratic,cubic,and parametrically excited terms is considered.We introduce an active control,i.e.a linear delayed-position feedback control,to the system,and the effects of the delayed feedback on the dynamics of the system are studied qualitatively.First,the normal form method is proposed to investigate the dynamics of the system with varying delay.Then the second-order approximation of the periodic solution is obtained,and is used to predict the stability of the bifurcation branches and the variation of the number of solutions with varying time delay.It is found that time delay can make the trivial equilibrium lose its stability,and induce the multiple attractors coexisting in the system.Finally,the numerical results are obtained through the 4thorder Runge-Kutta and point-to-point mapping methods.The basins of attraction are classified.In addition,the quasi-periodic attractor time delay induces is also obtained.The agreement of the numerical and theoretical results verifies the validity of the theoretical predictions.It is found that varying the delay can induce the complex dynamical behaviors in the system.This paper provides potential applications of these findings for the study of stabilization of controlled systems and chaotic motions." @default.
- W2377777621 created "2016-06-24" @default.
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- W2377777621 date "2010-01-01" @default.
- W2377777621 modified "2023-09-27" @default.
- W2377777621 title "Complex Dynamics of a Parametrically Excited System with Delayed Position Feedbacks" @default.
- W2377777621 hasPublicationYear "2010" @default.
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