摘要
The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic function.Then,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be negative.The effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically.
The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo＇s definition is analyzed.First,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic function.Then,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be negative.The effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically.
基金
supported by the National Natural Science Foundation of China(Grant Nos.10932009,11072212 and 11002059)
the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103501120003)
the Natural Science Foundation of Fujian Province (Grant No.2010J05006)
the Fundamental Research Funds for Huaqiao University(Grant No.JB-SJ1010)
the Research & Development Start Funds of Huaqiao University(Grant No.09BS622)
