This paper investigates the oscillatory and nonoscillatory behaviour of solu- tions of a class of third order nonlinear differential equations. Results extend and improve some known results in the literature.
In this paper, the asymptotical behaviour solutions of a class of nonlinear control systems are studied. By establishing infinite integrals along solutions of the system and drawing support from a LaSalle's invari...In this paper, the asymptotical behaviour solutions of a class of nonlinear control systems are studied. By establishing infinite integrals along solutions of the system and drawing support from a LaSalle's invariance principle of integral form, criteria of dichotomy and global asymptotical behaviour of solutions are obtained. This work is an improvement and further extension of research methods and results of A. S. Aisagaliev.展开更多
From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretica...From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series truncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.展开更多
The chaotic behaviour exhibited by a typical ferroresonant circuit in a neutral grounding system is investigated in this paper. In most earlier ferroresonance studies the core loss of the power transformer was neglect...The chaotic behaviour exhibited by a typical ferroresonant circuit in a neutral grounding system is investigated in this paper. In most earlier ferroresonance studies the core loss of the power transformer was neglected or represented by a linear resistance. However, this is not always true. In this paper the core loss of the power transformer is modelled by a third order series in voltage and the magnetization characteristics of the transformer are modelled by an llth order two-term polynomial. Extensive simulations are carried out to analyse the effect of nonlinear core loss on transformer ferroresonance. A detailed analysis of simulation results demonstrates that, with the nonlinear core loss model used, the onset of chaos appears at a larger source voltage and the transient duration is shorter.展开更多
This paper deals with oscillatory /nonoscillatory behaviour of solutions of thirdorder nonlinear differential equations of the formwhere a,b,c E C([a,oo),R) such that a(t) does not change sign, b(t) 5 0, c(t) > 0,f...This paper deals with oscillatory /nonoscillatory behaviour of solutions of thirdorder nonlinear differential equations of the formwhere a,b,c E C([a,oo),R) such that a(t) does not change sign, b(t) 5 0, c(t) > 0,f∈C(R, R) such that (f(y)/y) ≥ β > 0 for y ≠ 0 and γ > 0 is a quotient of odd integers.It has been shown, under certain conditions on coefficient functions, that a solution of (1)and (2) which Las a zero is oscillatory and the nonoscillatory solutions of these equationstend to zero as t → ∞. The motivation for this work came from the observation that thewhere al b, c are constants such that b≤ 0, c > 0, has an oscillatory solution if and only ifand all nonoscillatory solutions of (3) tend to zero if and only if the equation has anoscillatory solution.展开更多
By virtue of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of annihilation and creation operators of f-oscillator, this paper obtains two new types of ...By virtue of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of annihilation and creation operators of f-oscillator, this paper obtains two new types of squeezed operators and f-analogues of squeezed one-photon states, which are quite different from ones constructed by Song and Fan （Phys. Lett. A 294 （2002） 66）. Subsequently, some nonclassical properties of the states are investigated in detail.展开更多
文摘This paper investigates the oscillatory and nonoscillatory behaviour of solu- tions of a class of third order nonlinear differential equations. Results extend and improve some known results in the literature.
文摘In this paper, the asymptotical behaviour solutions of a class of nonlinear control systems are studied. By establishing infinite integrals along solutions of the system and drawing support from a LaSalle's invariance principle of integral form, criteria of dichotomy and global asymptotical behaviour of solutions are obtained. This work is an improvement and further extension of research methods and results of A. S. Aisagaliev.
文摘From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series truncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.
文摘The chaotic behaviour exhibited by a typical ferroresonant circuit in a neutral grounding system is investigated in this paper. In most earlier ferroresonance studies the core loss of the power transformer was neglected or represented by a linear resistance. However, this is not always true. In this paper the core loss of the power transformer is modelled by a third order series in voltage and the magnetization characteristics of the transformer are modelled by an llth order two-term polynomial. Extensive simulations are carried out to analyse the effect of nonlinear core loss on transformer ferroresonance. A detailed analysis of simulation results demonstrates that, with the nonlinear core loss model used, the onset of chaos appears at a larger source voltage and the transient duration is shorter.
文摘This paper deals with oscillatory /nonoscillatory behaviour of solutions of thirdorder nonlinear differential equations of the formwhere a,b,c E C([a,oo),R) such that a(t) does not change sign, b(t) 5 0, c(t) > 0,f∈C(R, R) such that (f(y)/y) ≥ β > 0 for y ≠ 0 and γ > 0 is a quotient of odd integers.It has been shown, under certain conditions on coefficient functions, that a solution of (1)and (2) which Las a zero is oscillatory and the nonoscillatory solutions of these equationstend to zero as t → ∞. The motivation for this work came from the observation that thewhere al b, c are constants such that b≤ 0, c > 0, has an oscillatory solution if and only ifand all nonoscillatory solutions of (3) tend to zero if and only if the equation has anoscillatory solution.
基金Project supported by the National Natural Science Foundation of China （Grant No 10574060） and the Natural Science Foundation of Shandong Province, China （Grant No Y2004A09）.
文摘By virtue of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of annihilation and creation operators of f-oscillator, this paper obtains two new types of squeezed operators and f-analogues of squeezed one-photon states, which are quite different from ones constructed by Song and Fan （Phys. Lett. A 294 （2002） 66）. Subsequently, some nonclassical properties of the states are investigated in detail.
