共查询到20条相似文献,搜索用时 15 毫秒
1.
S Rajasekar 《Pramana》1993,41(4):295-309
This paper investigates the possibility of controlling horseshoe and asymptotic chaos in the Duffing-van der Pol oscillator
by both periodic parametric perturbation and addition of second periodic force. Using Melnikov method the effect of weak perturbations
on horseshoe chaos is studied. Parametric regimes where suppression of horseshoe occurs are predicted. Analytical predictions
are demonstrated through direct numerical simulations. Starting from asymptotic chaos we show the recovery of periodic motion
for a range of values of amplitude and frequency of the periodic perturbations. Interestingly, suppression of chaos is found
in the parametric regimes where the Melnikov function does not change sign. 相似文献
2.
Bifurcations and chaos in the ubiquitous Duffing oscillator equation with different external periodic forces are studied numerically.
The external periodic forces considered are sine wave, square wave, rectified since wave, symmetric saw-tooth wave, asymmetric
saw-tooth wave, rectangular wave with amplitude-dependent width and modulus of sine wave. Period doubling bifurcations, chaos,
intermittency, periodic windows and reverse period doubling bifurcations are found to occur due to the applied forces. A comparative
study of the effect of various forces is performed. 相似文献
3.
V. Ravichandran S. Jeyakumari V. Chinnathambi S. Rajasekar M. A. F. Sanjuán 《Pramana》2009,72(6):927-937
Duffing oscillator driven by a periodic force with three different forms of asymmetrical double-well potentials is considered.
Three forms of asymmetry are introduced by varying the depth of the left-well alone, location of the minimum of the left-well
alone and above both the potentials. Applying the Melnikov method, the threshold condition for the occurrence of horseshoe
chaos is obtained. The parameter space has regions where transverse intersections of stable and unstable parts of left-well
homoclinic orbits alone and right-well orbits alone occur which are not found in the symmetrical system. The analytical predictions
are verified by numerical simulation. For a certain range of values of the control parameters there is no attractor in the
left-well or in the right-well. 相似文献
4.
In this Letter, nonlinear dynamic and chaotic behaviors of electrostatically actuated MEMS resonators subjected to random disturbance are investigated analytically and numerically. A reduced-order model, which includes nonlinear geometric and electrostatic effects as well as random disturbance, for the resonator is developed. The necessary conditions for the rising of chaos in the stochastic system are obtained using random Melnikov approach. The results indicate that very rich random quasi-periodic and chaotic motions occur in the resonator system. The threshold of bounded noise amplitude for the onset of chaos in the resonator system increases as the noise intensity increases. 相似文献
5.
We investigate an attractive Bose-Einstein condensate perturbed by a weak traveling optical superlattice. It is demonstrated
that under a stochastic initial set and in a given parameter region solitonic chaos appears with a certain probability that
is tightly related to the zero-point number of the Melnikov function; the latter depends on the potential parameters. Effects
of the lattice depths and wave vectors on the chaos probability are studied analytically and numerically, and different chaotic
regions of the parameter space are found. The results suggest a feasible method for strengthening or weakening chaos by modulating
the potential parameters experimentally.
相似文献
6.
7.
WANG Yan-Qun WU Qin 《理论物理通讯》2007,48(3):477-480
The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the lst-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos. When the parametric and external forces are strong, numerical simulations show that increasing the amplitude of the parametric or external force can lead the system into chaos via period doubling. 相似文献
8.
References: 《理论物理通讯》2007,48(9):477-480
The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the 1st-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos. When the parametric and external forces are strong, numerical simulations show that increasing the amplitude of the parametric or external force can lead the system into chaos via period doubling. 相似文献
9.
In this paper, the dynamics from the shock compacton to chaos in the nonlinearly Schrödinger equation with a source term is investigated in detail. The existence of unclosed homoclinic orbits which are not connected with the saddle point indicates that the system has a discontinuous fiber solution which is a shock compacton. We prove that the shock compacton is a weak solution. The Melnikov technique is used to detect the conditions for the occurrence from the shock compacton to chaos and further analysis of the conditions for chaos suppression. The results show that the system turns to chaos easily under external disturbances. The critical parameter values for chaos appearing are obtained analytically and numerically using the Lyapunov exponents and the bifurcation diagrams. 相似文献
10.
11.
掺杂超晶格是对同一材料交替掺入n-型和p-型杂质,形成n-i-p-i-n-i-p-i…一维阵列的周期结构。由于交替掺杂,衬底材料的导带受到周期调制形成一个个十分类似于正弦平方形式的量子阱。引入正弦平方势,在经典力学框架内,把粒子的运动方程化为具有阻尼项和受迫项的广义摆方程。用Jacobian椭圆函数和第一类全椭圆积分找到了无扰动系统的解和粒子振动周期,利用Melnikov方法分析了系统的全局分叉与Smale马蹄变换意义上的混沌行为,给出了系统通过级联分叉进入混沌的临界值。结果表明,对于异宿轨道,当参数满足条件 <πsech 时,系统出现了Smale马蹄变换意义上的混沌振荡。对于振荡型周期轨道,当参数满足条件 <πsech 时,产生了奇阶振荡型次谐分叉。注意到系统进入混沌的临界条件与它的参数有关,只需适当调节这些参数就可以避免或控制混沌,为光学双稳态器件的设计提供了理论分析。 相似文献
12.
13.
Chacón R Martínez García-Hoz A 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》1999,59(6):6558-6568
We study a parametrically damped two-well Duffing oscillator, subjected to a periodic string of symmetric pulses. The order-chaos threshold when altering solely the width of the pulses is investigated theoretically through Melnikov analysis. We show analytically and numerically that most of the results appear independent of the particular wave form of the pulses provided that the transmitted impulse is the same. By using this property, the stability boundaries of the stationary solutions are determined to first approximation by means of an elliptic harmonic balance method. Finally, the bifurcation behavior at the stability boundaries is determined numerically. 相似文献
14.
本文用Melnikov方法得到了含二次非线性项受迫振动系统的混沌阈值,分析了参数对阈值的影响,与以往用近似二维叠代和数值积分的结果进行了比较。
关键词: 相似文献
15.
The chaotic dynamics of nonlinear waves in the harmonic-forced fluid-conveying pipe in primary parametrical resonance, is explored analytically and numerically. The multiple scale method is applied to obtain an equivalent nonlinear wave equation from the complicated nonlinear governing equation describing the fluid conveyed in a pipe. With the Melnikov method, the persistence of a heteroclinic structure is shown to be satisfied and its condition is given in functional form. Similarly, for the heteroclinic orbit, using geometric analysis, a condition function of the stable manifold is derived for the orbit to return to the stable manifold from the saddle point. The persistent homoclinic structures and threshold of chaos in the Smale-horseshoe sense are obtained for the fluid-conveying pipe under both conditions, indicating how the external excitation amplitude can change substantially the global dynamics of the fluid conveyed in the pipe. A numerical approach was used to test the prediction from theory. The impact of the external excitation amplitude on the nonlinear wave in the fluid-conveying pipe was also studied from numerical simulations. Both theoretical predications and numerical simulations attest to the complex chaotic motion of fluid-conveying pipes. 相似文献
16.
F. Li W. X. Shu J. G. Jiang H. L. Luo Z. Ren 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,41(2):355-361
Spatiotemporal dynamics of Bose-Einstein condensates in
moving optical lattices have been studied. For a weak lattice
potential, the perturbed correction to the heteroclinic orbit in a
repulsive system is constructed. We find the boundedness
conditions of the perturbed correction contain the Melnikov
chaotic criterion predicting the onset of Smale-horseshoe chaos.
The effect of the chemical potential on the spatiotemporal
dynamics is numerically investigated. It is revealed that the
variance of the chemical potential can lead the systems into
chaos. Regulating the intensity of the lattice potential can
efficiently suppress the chaos resulting from the variance of the
chemical potential. And then the effect of the phenomenological
dissipation is considered. Numerical calculation reveals that the
chaos in the dissipative system can be suppressed by adjusting the
chemical potential and the intensity of the lattice potential. 相似文献
17.
F. Li B. J. Zhou W. X. Shu H. L. Luo Z. Y. Huang L. Tian 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,50(1):75-80
We study the chaotic dynamics of a parametrically
modulated Josephson junction with quadratic damping. The Melnikov
chaotic criteria are presented. When the perturbation conditions
cannot be satisfied, numerical simulations demonstrate that the
system can step into chaos via a quasi-periodic route with the
increasing of the dc component of the modulation. However, it is
numerically demonstrated that adding a feedback to the system can
effectively suppress the chaos. 相似文献
18.
C.H. Miwadinou A.V. Monwanou J. Yovogan L.A. Hinvi P.R. Nwagoum Tuwa J.B. Chabi Orou 《Chinese Journal of Physics (Taipei)》2018,56(3):1089-1104
This paper addresses the issues of nonlinear chemical dynamics modeled by a modified Van der Pol-Duffing oscillator with asymmetric potential. The Melnikov method is utilized to analytically determine the domains boundaries where Melnikov’s chaos appears in chemical oscillations. Routes to chaos are investigated through bifurcations structures, Lyapunov exponent, phase portraits and Poincaré section. The effects of parameters in general and in particular the effect of the constraint parameter β which shows the difference between a nonlinear chemical dynamics order two differential equation and ordinary Van der Pol-Duffing equation are analyzed. Results of analytical investigations are validated and complemented by numerical simulations. 相似文献
19.
For the Melnikov theory of chaos, the second-order approximation is given. Applying the result to the dynamics system with quadratic nonlinear term, it is shown that the threshold of chaos depends on initial condition and can be greater than that of the Melnikov method. The first order variational equations of some nonlinear dynamical systems are all the second-order ordinary differential equations with hyperbolic cosine function, its solution is given. 相似文献