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排序方式: 共有303条查询结果,搜索用时 31 毫秒
61.
We study the phase topology of a new Liouville integrable Hamiltonian system with an additional quartic integral (the Sokolov case). 相似文献
62.
N. D. Stein 《Journal of statistical physics》1989,56(5-6):841-878
A four-mode model of convection in a rotating fluid layer is studied. The model is an extension of the Lorenz model of Rayleigh-Bénard convection, the extra mode accounting for the regeneration of vorticity by rotation. Perturbation theory is applied to show that the Hopf bifurcations from conductive and steady convective solutions can be either supercritical or subcritical. Perturbation theory is also used at large Rayleigh numbersr to predict novel behavior. Supercritical oscillatory convection of finite amplitude is found by numerical integration of the governing equations. The general picture is of a series of oscillatory solutions stable over larger intervals, interspersed by short bursts of chaos. 相似文献
63.
Sue Ann Campbell Jacques Bélair Toru Ohira John Milton 《Journal of Dynamics and Differential Equations》1995,7(1):213-236
We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The bifurcations occurring as the linear stability is lost are investigated by the construction of a center manifold: The nature of Hopf bifurcations and more degenerate, higher-codimension bifurcations are explicitly determined. 相似文献
64.
Summary Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put
the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences of relaxing
the restrictions of the form of the coordinate transformations. In the Duffing equation, a logarithmic transformation can
remove the nonlinearity: in one interpretation, the nonlinearity is replaced by a branch cut leading to a Poincaré section.
When the linearized problem is autonomous with diagonal Jordan form, we can remove all nonlinearities order by order using
these singular coordinate transformations.
Deceased, November 4, 1993. 相似文献
65.
66.
I. I. Fedchenia 《Journal of statistical physics》1988,52(3-4):1005-1029
By an example of a two-dimensional hydrodynamic system, second-order Langevin equations with two correlated noise sources are investigated. It is shown that the asymptotic expression (t) for the stationary distribution functionP depends on the order in which the limiting transitions;t andN
220 (N
22 is the power of one of the noises) are made. Using the method of local expansions in trigonometric form, approximate expressions are written for the distribution functionP at small but finiteN
22 tending atN
220 to the known exact solution. 相似文献
67.
In this paper we study the Navier-Stokes flow on the two-dimensional torusS
1
×S
1 excited by the external force (k
2 sinky, 0) and find the long-time behavior for the flow starting from some states, whereS
1=[0,2](mod 2). Especially for the casek=2, it follows from an analysis and computation that the Navier-Stokes flow with the initial state cos(mx+ny) or sin(mx+ny) will likely evolve through at most one step bifurcation to either a steady-state solution or a time-dependent periodic solution for any Reynolds number and integersm andn. 相似文献
68.
Dynamical behaviors of Liu system is studied using Routh–Hurwitz criteria, Center manifold theorem and Hopf bifurcation theorem. Periodic solutions and their stabilities about the equilibrium points are studied by using Hsü & Kazarinoff theorem. Linear feedback control techniques are used to stabilize and synchronize the chaotic Liu system. 相似文献
69.
Bifurcations of a degenerate homoclinic orbit with orbit flip in high dimensional system are studied. By establishing a local
coordinate system and a Poincaré map near the homoclinic orbit, the existence and uniqueness of 1–homoclinic orbit and 1–periodic
orbit are given. Also considered is the existence of 2–homoclinic orbit and 2–periodic orbit. In additon, the corresponding
bifurcation surfaces are given.
Project supported by the National Natural Science Foundation of China (No: 10171044), the Natural Science Foundation of Jiangsu
Province (No: BK2001024), the Foundation for University Key Teachers of the Ministry of Education of China 相似文献
70.
Weakly coupled CML can be analytically solved by using perturbative methods. This technique has been recently used to deduce analytical expressions for travelling waves. Nonetheless, the results were limited for periodic solutions far away from saddle-node bifurcation. In this Letter, this problem is solved and periodic solutions, arising from the individual dynamics, are totally characterised. 相似文献