A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,w...A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,which is expressed by complex amplitudes,of the first order is obtained.And solvable conditions satisfied by the complex amplitudes are given,and then the relative result is generalized.展开更多
For a co_dimension two bifurcation system on a three_dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a ...For a co_dimension two bifurcation system on a three_dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system_a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker_Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.展开更多
For a real noise parametrically excited co_dimension two bifurcation system on a three_dimensional central manifold, a model of enhanced generality is developed in the present paper by assuming the real noise to be an...For a real noise parametrically excited co_dimension two bifurcation system on a three_dimensional central manifold, a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system, namely,a zero_mean stationary Gaussian diffusion process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker_Planck operator.展开更多
One of the key. problems in the nonlinear theory of the hydrodynamic stability isto determine the law of the evolution of the disiurbance velocity amplitude. The methods, which have been obtained, can only, be u...One of the key. problems in the nonlinear theory of the hydrodynamic stability isto determine the law of the evolution of the disiurbance velocity amplitude. The methods, which have been obtained, can only, be usedfor quasi-neuiral flow and havesome artificial faciors. In this paper, a method is proposed for this problm.展开更多
In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
基金Supported by the NNSF of China(10471039)Supported by the Natural Science Foundation of Zhejiang Province(Y606268)Supported by the E-Institutes of Shanghai Municipal Education Commission(E03004)
文摘A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,which is expressed by complex amplitudes,of the first order is obtained.And solvable conditions satisfied by the complex amplitudes are given,and then the relative result is generalized.
文摘For a co_dimension two bifurcation system on a three_dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system_a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker_Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.
基金the National Natural Science Foundation of China
文摘For a real noise parametrically excited co_dimension two bifurcation system on a three_dimensional central manifold, a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system, namely,a zero_mean stationary Gaussian diffusion process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker_Planck operator.
文摘One of the key. problems in the nonlinear theory of the hydrodynamic stability isto determine the law of the evolution of the disiurbance velocity amplitude. The methods, which have been obtained, can only, be usedfor quasi-neuiral flow and havesome artificial faciors. In this paper, a method is proposed for this problm.
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
