Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincare map and the method of rescaling a discriminating condition for th...Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincare map and the method of rescaling a discriminating condition for the existence of subharmonic solutions of order m is obtained. An example is given in the end of the paper.展开更多
This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-...This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.展开更多
The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z（t） = JVH...The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z（t） = JVH（t, z（t））, where H（t, z） = 1/2（B（t）z, z） ＋ H（t, z）, B（t） is a semipositive symmetric continuous matrix and H is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.展开更多
The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elli...The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.展开更多
Some global behavior for a slowly varying oscillator was investigated. Based on a series of transformations and the theory of periodic orbits and integral manifold, the bifurcations of subharmonic solutions and invari...Some global behavior for a slowly varying oscillator was investigated. Based on a series of transformations and the theory of periodic orbits and integral manifold, the bifurcations of subharmonic solutions and invariant tori generated from a semistable limit cycle in the fast dynamics were discussed.展开更多
This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in ...This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies g(x,t/x+, as|x| - +. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions.展开更多
文摘Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincare map and the method of rescaling a discriminating condition for the existence of subharmonic solutions of order m is obtained. An example is given in the end of the paper.
基金Project supported by the National Natural Science Foundation of China (No. 10671214)the Chongqing Natural Science Foundation of China (No. 2005cc14)Shanghai Shuguang Genzong Project (No.04SGG05)
文摘This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.
基金supported by the National Natural Science Foundation of China(Nos.11501030,11226156)the Beijing Natural Science Foundation(No.1144012)
文摘The author mainly uses the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the Hamiltonian systems z（t） = JVH（t, z（t））, where H（t, z） = 1/2（B（t）z, z） ＋ H（t, z）, B（t） is a semipositive symmetric continuous matrix and H is unbounded and not uniformly coercive. It is proved that when the positive integers j and k satisfy the certain conditions, there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.
文摘The problem of nonlinear forced oscillations for elliptical sandwich plates is dealt with. Based on the governing equations expressed in terms of five displacement components, the nonlinear dynamic equation of an elliptical sandwich plate under a harmonic force is derived. A superpositive-iterative harmonic balance (SIHB) method is presented for the steady-state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as fundamental differential equation with fundamental harmonics and incremental differential equation with derived harmonics. The 1/3 subharmonic solution of an elliptical sandwich plate is investigated by using the methods of SIHB. The SIHB method is compared with the numerical integration method. Finally, asymptotical stability of the 1/3 subharmonic oscillations is inspected.
文摘Some global behavior for a slowly varying oscillator was investigated. Based on a series of transformations and the theory of periodic orbits and integral manifold, the bifurcations of subharmonic solutions and invariant tori generated from a semistable limit cycle in the fast dynamics were discussed.
文摘This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies g(x,t/x+, as|x| - +. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions.
