The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the lst-order equation. Through the boun...The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the lst-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos. When the parametric and external forces are strong, numerical simulations show that increasing the amplitude of the parametric or external force can lead the system into chaos via period doubling.展开更多
This paper deals with an integral transformation involving Whittaker function Mk,m（X） into a multiple hypergeometric series of Lauricella function FA（n） of n variables. A number of known and new transformation and...This paper deals with an integral transformation involving Whittaker function Mk,m（X） into a multiple hypergeometric series of Lauricella function FA（n） of n variables. A number of known and new transformation and reduction formulae for a hypergeometric function 2F1, Appell function F2, Lauricella function FA（3） and a hypergeometric function of four variables Fp（4） are derived as special cases.展开更多
文摘The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the lst-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos. When the parametric and external forces are strong, numerical simulations show that increasing the amplitude of the parametric or external force can lead the system into chaos via period doubling.
文摘This paper deals with an integral transformation involving Whittaker function Mk,m（X） into a multiple hypergeometric series of Lauricella function FA（n） of n variables. A number of known and new transformation and reduction formulae for a hypergeometric function 2F1, Appell function F2, Lauricella function FA（3） and a hypergeometric function of four variables Fp（4） are derived as special cases.
