共查询到20条相似文献,搜索用时 0 毫秒
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We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean
and variance
are well-characterized functions of the noise statistics, and
and
depend on . When noise is continuously present along the trajectory,
and
are independent of the noise statistics and . However, in their evolution toward
and
, both
u
(t, x) and
u
2
(t, x) depend on the noise and. 相似文献
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S. V. Kiyashko 《Radiophysics and Quantum Electronics》2008,51(4):324-330
We study experimentally the dynamics of roll domains of the parametrically excited capillary waves. The domain rolls were
perpendicular to one another and parallel to different boundaries of a rectangular cuvette. It is found that depending on
the initial and boundary conditions, two-dimensional different-shape domains arise at the cuvette edges, and the dynamics
of the domain is determined by the motion of their fronts. A model of the observed phenomenon is proposed, which is used for
numerical calculations. Simulation results are in good agreement with the experimental evidence.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 359–366, April 2008. 相似文献
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The stability and bifurcation analyses of periodic motions in a rotating blade subject to a torsional excitation are investigated. For high speed rotations, cubic geometric nonlinearity and gyroscopic effects of the rotating blade are considered. From the Galerkin method, the partial differential equation of the nonlinear rotating blade is simplified to the ordinary differential equations, and periodic motions and stability of the rotating blade are studied by the generalized harmonic balance method. The analytical and numerical results of periodic solutions are compared. The rich dynamics and co-existing periodic solutions of the nonlinear rotating blades are investigated. 相似文献
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The paper is concerned with a set of linear differential equations with time-dependent parameters given by trigonometrical series. Derived formulas make it possible to examine stability, to find boundaries of the regions of instability and to estimate the steady state response amplitude of forced vibrations. 相似文献
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In this paper,the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are studied.The damping,parametrical excitation and the nonlinearities are regarded as weak.The averaged equation depicting the fast and slow dynamics is derived through the method of multiple scales.The dynamics near the resonance band is revealed by doing a singular perturbation analysis and combining the extended Melnikov method.We are able to determine the criterion for the existence of the multi-pulse homoclinic orbits which can form the Shilnikov orbits and give rise to chaos.At last,numerical results are also given to illustrate the nonlinear behaviors and chaotic motions in the nonlinear nano-oscillator. 相似文献
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We present analytical and numerical study of high-order parametric resonance in a driven magneto-optical trap of cold atoms. We have obtained the general solutions for parametric resonance of arbitrary order. In particular, the amplitude and phase of atomic limit-cycle motion is expressed as a function of the modulation amplitude and frequency. Moreover, the atomic dynamics for high-order parametric resonance is investigated in terms of the Hamiltonian approach, which is useful in studying transitions between attractors. We find that the analytical results are in good agreement with the numerical calculations. 相似文献
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We find concrete evidence for a recently discovered form of intermittency, referred to as in-out intermittency, in both partial differential equation (PDE) and ordinary differential equation (ODE) models of mean field dynamos. This type of intermittency [introduced in P. Ashwin, E. Covas, and R. Tavakol, Nonlinearity 9, 563 (1999)] occurs in systems with invariant submanifolds and, as opposed to on-off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behavior may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in-out intermittency are axisymmetric mean-field dynamo models which are often used to study the observed large-scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities. (c) 2001 American Institute of Physics. 相似文献
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Bifurcations of a parametrically excited oscillator with strong nonlinearity 总被引:4,自引:0,他引:4 下载免费PDF全文
A parametrically excited oscillator with strong nonlinearity, including van der Pol and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt-Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed. 相似文献
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The present paper studies the pulse narrowing nonlinear transmission lines equation, describing pulse narrowing in the field of communication engineering. More precisely, the pulse narrowing nonlinear transmission line equation is solved analytically using the recently developed techniques viz the modified Kudraysov method, the sine-Gordon equation expansion method and the extended sinh-Gordon equation expansion method. As a result, a wide range of dark, bright, dark–bright, singular or combined singular and optical soliton solutions for the pulse narrowing nonlinear transmission lines equation is formally obtained. All solutions have been verified back into its corresponding equation with the aid of maple package program. 相似文献
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Yvette Kosmann-Schwarzbach 《Letters in Mathematical Physics》1979,3(5):395-404
We propose a rigorous definition of the generalized infinitesimal symmetries using the notion of k-vector fields, and we derive an algorithm for their determination. We show that Bäcklund transformations between evolution equations are differential operators having prescribed symmetries. 相似文献
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Sandweg CW Kajiwara Y Chumak AV Serga AA Vasyuchka VI Jungfleisch MB Saitoh E Hillebrands B 《Physical review letters》2011,106(21):216601
We experimentally show that exchange magnons can be detected by using a combination of spin pumping and the inverse spin-Hall effect proving its wavelength integrating capability down to the submicrometer scale. The magnons were injected in a ferrite yttrium iron garnet film by parametric pumping and the inverse spin-Hall effect voltage was detected in an attached Pt layer. The role of the density, wavelength, and spatial localization of the magnons for the spin pumping efficiency is revealed. 相似文献
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Here cell population dynamics in which there is simultaneous proliferation and maturation is considered. The resulting mathematical model is a nonlinear first-order partial differential equation for the cell density u(t,x) in which there is retardation in both temporal (t) and maturation variables (x), and contains three parameters. The solution behavior depends on the initial function varphi(x) and a three component parameter vector P=(delta,lambda,r). For strictly positive initial functions, varphi(0) greater, similar 0, there are three homogeneous solutions of biological (i.e., non-negative) importance: a trivial solution u(t) identical with 0, a positive stationary solution u(st), and a time periodic solution u(p)(t). For varphi(0)=0 there are a number of different solution types depending on P: the trivial solution u(t), a spatially inhomogeneous stationary solution u(nh)(x), a spatially homogeneous singular solution u(s), a traveling wave solution u(tw)(t,x), slow traveling waves u(stw)(t,x), and slow traveling chaotic waves u(scw)(t,x). The regions of parameter space in which these solutions exist and are locally stable are delineated and studied. 相似文献
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In this paper, we improve some key steps in the homogeneous balance method (HBM), and propose a modified homogeneous balance
method (MHBM) for constructing multiple soliton solutions of the nonlinear partial differential equation (PDE) in a unified
way. The method is very direct and primary; furthermore, many steps of this method can be performed by computer. Some illustrative
equations are investigated by this method and multiple soliton solutions are found. 相似文献