共查询到19条相似文献,搜索用时 125 毫秒
1.
本文用随机模拟方法研究了一化学混沌模型的介观动力学。对该混沌模型的系综模拟发现 ,在这种不稳定运动中存在强烈的内部涨落 ,然而由于混沌运动整体上的稳定性 ,使得系统中的代表点被限制在混沌吸引子上 ,并且每个代表点形成的随机轨道很好地保持了确定性混沌吸引子的基本特性 相似文献
2.
研究了叉形分岔系统和FitzHugh Nagumo(FHN)细胞模型两种非线性动力系统分岔点邻域内 随机共振的特性.研究结果表明:这两种系统在分岔发生时具有由一个吸引子变为两个吸引 子或者由两个吸引子变为一个吸引子共同的分岔特性,即在分岔点的邻域内, 系统在分岔点 的两侧有分岔前吸引子和分岔后吸引子存在,在噪声的作用下,系统的运动除了像传统随机 共振的机理那样在分岔点一侧共存的吸引子之间跃迁,还在分岔点两侧三个吸引子(分岔前 一个吸引子和分岔后两个吸引子)之间跃迁,并且这种跃迁单独诱发了随机共振 ;在两种 跃迁都发生的情况下, 在其分岔点的邻域内,由第二种跃迁诱发的随机共振在引起第一种跃 迁噪声的强度很大的范围内变化仍可维持, 而第一种跃迁诱发的随机共振在引起第二种跃迁 噪声的强度很小的范围内变化即迅速消失.
关键词:
随机共振
吸引子
分岔点
跃迁 相似文献
3.
应用广义胞映射图论方法研究常微分方程系统的激变.揭示了边界激变是由于混沌吸引子与 在其吸引域边界上的周期鞍碰撞产生的,在这种情况下,当系统参数通过激变临界值时,混 沌吸引子连同它的吸引域突然消失,在相空间原混沌吸引子的位置上留下了一个混沌鞍.研 究混沌吸引子大小(尺寸和形状)的突然变化,即内部激变.发现这种混沌吸引子大小的突然 变化是由于混沌吸引子与在其吸引域内部的混沌鞍碰撞产生的,这个混沌鞍是相空间非吸引 的不变集,代表内部激变后混沌吸引子新增的一部分.同时研究了这个混沌鞍的形成与演化. 给出了对永久自循环胞集和瞬态自循环胞集进行局部细化的方法.
关键词:
广义胞映射
有向图
激变
混沌鞍 相似文献
4.
利用Lyapunov指数和分岔图研究了运动光学晶格中的Bose-Einstein condensate(BEC)粒子数密度的时空演化.数值分析了从周期运动改变到混沌运动的各种吸引子及相应的时间变化图,本文从理论上和数值模拟上来研究BEC的混沌性质. 相似文献
5.
在分段光滑模型的基础上,推导出基于比例积分(PI)控制的电压反馈型Buck变换器的光滑模型及离散迭代模型.证明了功率系统的混沌吸引子在负载线上运动,并受到占空比的控制,模型的流形围绕吸引子运动并出现1周期、2周期及混沌现象;推导出电压反馈型PI控制系统的输出电压与Buck变换器的输出电压成线性关系,在此基础上指出PI控制中的比例因子起主导作用;分析了系统的倍周期分岔、边界碰撞和混沌现象,并展示了变换器状态的转移过程.实验结果表明了理论建模分析和仿真的正确性. 相似文献
6.
7.
利用Lyapunov指数和分岔图研究了运动光学晶格中的Bose-Einstein condensate(BEC)粒子数密度的时空演化.数值分析了从周期运动改变到混沌运动的各种吸引子及相应的时间变化图,本文从理论上和数值模拟上来研究BEC的混沌性质. 相似文献
8.
本文提出并研究了在剪切磁场中非理想MHD流的Rayleigh-Bnard问题的一个模型,得到了关于这个模型的一个新的非线性微分方程组。理论和数值分析表明:这组方程蕴含一个奇异吸引子,它具有不同于Lorenz吸引子的一些新特性;更重要的是,已知的三条通往混沌的道路并存于这个模型之中。应当指出,在迄今所有已知的向混沌态过渡的三条道路共存的模型中,我们的方程组是唯一没有外部周期驱动项的,更直接地体现了非线性确定论系统的“内在”随机件、另外,对这个简单模型进行数值模拟.我们观察到磁力线的随机运动、磁力线重联和磁岛
关键词: 相似文献
9.
近期文献中报道了在具有自适应反馈突触的神经元模型中,随着参数的变化,存在从两个共存吸引子到一个相连吸引子再到两个共存吸引子的混沌转化现象.本文对此模型进行了电路设计,同时对具有非单调激活函数功能的电路设计进行了细致的研究,并利用Electronic Workbench (EWB)软件对所设计的电路进行了仿真实验,研究了电路中的混沌现象,验证了所设计电路的动力学行为与通过数值模拟结果十分相似.
关键词:
自适应反馈突触
神经元模型
混沌
电路设计 相似文献
10.
11.
The dynamics of transport at the edge of magnetized plasmas is deterministic chaos. The connection is made by a previous survey [M. A. Pedrosa et al., Phys. Rev. Lett. 82, 3621 (1999)] of measurements of fluctuations that is shown to exhibit power spectra with exponential frequency dependence over a broad range, which is the signature of deterministic chaos. The exponential character arises from Lorentzian pulses. The results suggest that the generalization to complex times used in studies of deterministic chaos is a representation of Lorentzian pulses emerging from the chaotic dynamics. 相似文献
12.
讨论了具有有界随机参数的随机Bonhoeffer-Van der Pol系统的随机混沌现象,并利用噪声对其进行控制.首先运用Chebyshev多项式逼近的方法,将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统,使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题,继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题.数值结果表明,随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似.利用噪声控制法可将混沌控制到周期轨道,但是在随机参数及其强度的影响下也呈现出一些特点. 相似文献
13.
Analysis of stochastic bifurcation and chaos in stochastic Duffing-van der Pol system via Chebyshev polynomial approximation 下载免费PDF全文
The Chebyshev polynomial approximation is applied to investigate the stochastic
period-doubling bifurcation and chaos problems of a stochastic Duffing--van
der Pol system with bounded random parameter of exponential probability
density function subjected to a harmonic excitation. Firstly the stochastic
system is reduced into its equivalent deterministic one, and then the
responses of stochastic system can be obtained by numerical methods.
Nonlinear dynamical behaviour related to stochastic period-doubling
bifurcation and chaos in the stochastic system is explored. Numerical
simulations show that similar to its counterpart in deterministic nonlinear
system of stochastic period-doubling bifurcation and chaos may occur in the
stochastic Duffing--van der Pol system even for weak intensity of random
parameter. Simply increasing the intensity of the random parameter may
result in the period-doubling bifurcation which is absent from the
deterministic system. 相似文献
14.
应用Laguerre正交多项式逼近法研究了含有随机参数的双势阱Duffing系统的分岔和混沌行为.系统参数为指数分布随机变量的非线性动力系统首先被转化为等价的确定性扩阶系统,然后通过数值方法求得其响应.数值模拟结果的比较表明,含有随机参数的双势阱Duffing系统保持着与确定性系统相类似的倍周期分岔和混沌行为,但是由于随机因素的影响,在局部小区域内随机参数系统的动力学行为会发生突变.
关键词:
双势阱Duffing系统
指数分布概率密度函数
Laguerre多项式逼近
随机分岔 相似文献
15.
神经元电活动理论模型Hindmarsh-Rose(HR)模型提示有位于周期1和周期2放电模式之间的一类特殊的混沌放电,但长期以来对其没有获得足够认识.依据回归映射的确定性结构和非线性预报的短期可预报性,确认了在大鼠的实验性神经起步点的实验中发现的位于周期1和周期2放电模式之间的非周期放电是混沌放电模式,还将该混沌放电模式区分为3个不同表观样式.其中1个表观形式与HR模型的仿真结果相类似,验证了HR模型的理论预期;其余2个样式与仿真结果并不相似.进一步揭示了3个表观样式的动力学特征以及相互之间的区别与联系,并与位于周期2和周期3节律之间、周期3和周期4节律之间的混沌比较了异同,也区别了从周期1到混沌再到周期2放电模式的节律转迁历程与其他的从周期1到周期2节律的分岔过程的不同.研究结果确认了该类特殊混沌节律和相应分岔过程的新特征,丰富了混沌放电节律和节律分岔序列的种类.还对仿真该混沌的多样性和非光滑特性,以及揭示该类混沌的产生途径等进行了讨论.
关键词:
混沌
神经放电模式
分岔
节律 相似文献
16.
M. Gosak M. Marhl M. Perc 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(2):171-177
We study the transition from stochasticity to determinism
in calcium oscillations via diffusive coupling of individual cells that are
modeled by stochastic simulations of the governing reaction-diffusion
equations. As expected, the stochastic solutions gradually converge to their
deterministic limit as the number of coupled cells increases. Remarkably
however, although the strict deterministic limit dictates a fully periodic
behavior, the stochastic solution remains chaotic even for large numbers of
coupled cells if the system is set close to an inherently chaotic regime. On
the other hand, the lack of proximity to a chaotic regime leads to an
expected convergence to the fully periodic behavior, thus suggesting that
near-chaotic states are presently a crucial predisposition for the
observation of noise-induced chaos. Our results suggest that chaos may exist
in real biological systems due to intrinsic fluctuations and uncertainties
characterizing their functioning on small scales. 相似文献
17.
Pierre Suret Marc Lefranc Dominique Derozier Jaouad Zemmouri Serge Bielawski 《Optics Communications》2001,200(1-6):369-379
We report on the observation of fast oscillations at frequencies of a few MHz in a triply resonant optical parametric oscillator. These oscillations can appear alone, or superimposed on slow oscillations due to thermo-optical instabilities, and display a great variety of waveforms. The analysis of the regimes observed experimentally leads us to conjecture that the mechanism responsible for this instability is not the Hopf bifurcation of the single-mode mean-field model, but that it is based on the interaction of two signal fields oscillating in cavity modes with neighboring frequencies. This interpretation is supported by numerical simulations of the mean-field model with two coupled modes, which reproduce well the behaviors observed experimentally. We also find chaotic solutions of this model, which unveils another possible scenario leading to deterministic chaos in this system. 相似文献
18.
19.
M. Mulansky K. Ahnert A. Pikovsky D. L. Shepelyansky 《Journal of statistical physics》2011,145(5):1256-1274
We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear
oscillators by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos
is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being
proportional to the square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes.
In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which
drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this
weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices
of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes.
The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling
strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology. 相似文献