共查询到19条相似文献,搜索用时 96 毫秒
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研究了乘性非高斯噪声和加性高斯白噪声共同激励下FitzHugh-Nagumo(FHN) 神经元系统的随机共振问题. 利用路径积分法和两态模型理论, 推导出系统信噪比的表达式. 研究结果表明: 系统参数在不同的取值条件下, FHN神经元模型出现了随机共振和双重随机共振现象. 此外, 非高斯参数q在不同的取值条件下, 乘性噪声强度和加性噪声强度对信噪比的影响是不同的. 非高斯噪声的加入有利于增强FHN神经元系统的信号响应. 相似文献
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为了刻画在黏弹性介质中具有质量涨落的耦合粒子的运动行为,本文提出了相应模型,即三态噪声激励下的分数阶耦合系统.利用Shapiro-Loginov公式和Laplace变换,发现了粒子间的统计同步性,并得到了系统输出幅值增益的解析表达.在此基础上,针对模型涉及的关键要素,即耦合系统、分数阶系统和三态噪声,着重分析了耦合系数、系统阶数和噪声稳态转移概率对系统输出幅值增益的广义随机共振现象的影响,并给出了合理解释.具体地说,1)随着耦合系数的增大,共振现象将先增强后减弱,直至收敛.该现象表明适当的耦合作用能够促进系统共振现象的产生,体现了研究耦合系统的重要性.2)随着系统阶数的增大,共振现象将逐渐减弱.当系统阶数取值为1,即系统退化为整数阶系统时,其输出幅值增益的峰值最小,该现象说明分数阶系统能比传统整数阶系统得到更大的输出幅值增益.3)噪声稳态转移概率对系统输出幅值增益的影响会随着与之相关的其他参数的变化而变化.在一定参数条件下,三态噪声不仅能够使系统输出幅值获得比双态噪声激励时更大的增益,还能改变系统的共振类型.最后,通过数值仿真验证了上述结果的正确性. 相似文献
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研究了乘性色噪声作用下三稳态van der Pol-Duffing振子的随机P-分岔问题. 首先应用随机平均法得到系统振动幅值稳态概率密度函数的表达式, 进而应用奇异性理论, 得到刻画随机P-分岔发生的临界参数条件的转迁集以及系统存在的典型稳态概率密度曲线, 并通过Monte-Carlo数值模拟进行了验证. 以此为基础讨论了噪声强度、相关时间、系统线性阻尼系数对随机P-分岔和系统稳态响应行为的影响. 相似文献
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研究了Lévy稳定噪声激励下的双稳Duffing-van der Pol振子,利用Monte Carlo方法,得到了振幅的稳态概率密度函数.分析了Lévy稳定噪声的强度和稳定指数对概率密度函数的影响,通过稳态概率密度的性质变化,讨论了噪声振子的随机分岔现象,发现了不仅系统参数和噪声强度可以视为分岔参数,Lévy噪声的稳定指数 α 的改变也能诱导系统出现随机分岔现象.
关键词:
Lévy稳定噪声
Duffing-van der Pol振子
稳态概率密度函数
随机分岔 相似文献
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This paper undertakes a nonlinear analysis of a model for a maglev system with time-delayed feedback. Using linear analysis, we determine constraints on the feedback control gains and the time delay which ensure stability of the maglev system. We then show that a Hopf bifurcation occurs at the linear stability boundary. To gain insight into the periodic motion which arises from the Hopf bifurcation, we use the method of multiple scales on the nonlinear model. This analysis shows that for practical operating ranges, the maglev system undergoes both subcritical and supercritical bifurcations, which give rise to unstable and stable limit cycles respectively. Numerical simulations confirm the theoretical results and indicate that unstable limit cycles may coexist with the stable equilibrium state. This means that large enough perturbations may cause instability in the system even if the feedback gains are such that the linear theory predicts that the equilibrium state is stable. 相似文献
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Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback
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The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied.By considering the energy in the air-gap field of the AC motor,the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system.The characteristic roots and the stable regions of time delay are determined by the direct method,and the relationship between the feedback gain and the length summation of stable regions is analyzed.Choosing the time delay as a bifurcation parameter,we find that the Hopf bifurcation occurs when the time delay passes through a critical value.A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem.Numerical simulations are also performed,which confirm the analytical results. 相似文献
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Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation
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A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function (PDF) of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored. 相似文献
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Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system
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This paper investigates the stochastic resonance (SR)
phenomenon induced by the multiplicative periodic signal in a cancer
growth system with the cross-correlated noises and time delay. To
describe the periodic change of the birth rate due to the periodic
treatment, a multiplicative periodic signal is added to the system.
Under the condition of small delay time, the analytical expression
of the signal-to-noise ratio R_{\rm SNR} is derived in the
adiabatic limit. By numerical calculation, the effects of the
cross-correlation strength \lambda and the delay time \tau on
R_{\rm SNR} are respectively discussed. The existence of a peak in
the curves of R_{\rm SNR} as a function of the noise intensities
indicates the occurrence of the SR phenomenon. It is found that
\lambda and \tau play opposite role on the SR phenomenon, i.e.,
the SR is suppressed by increasing \lambda whereas it is enhanced
with the increase of \tau, which is different from the case where
the periodic signal is additive. 相似文献
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Direct time delay feedback can make non-chaotic Chen
circuit chaotic. The chaotic Chen circuit with direct time delay
feedback possesses rich and complex dynamical behaviours. To reach a
deep and clear understanding of the dynamics of such circuits
described by delay differential equations, Hopf bifurcation in the
circuit is analysed using the Hopf bifurcation theory and the
central manifold theorem in this paper. Bifurcation points and
bifurcation directions are derived in detail, which prove to be
consistent with the previous bifurcation diagram. Numerical
simulations and experimental results are given to verify the
theoretical analysis. Hopf bifurcation analysis can explain and
predict the periodical orbit (oscillation) in Chen circuit with
direct time delay feedback. Bifurcation boundaries are derived using
the Hopf bifurcation analysis, which will be helpful for determining
the parameters in the stabilisation of the originally chaotic
circuit. 相似文献
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The steady state response and bifurcation of nonlinear random business cycle model to random narrow-band excitation with time delay state feedback are studied in this paper. The method of multiple scales is used to determine the business cycle model of modulation of amplitude and phase. The effects of delay, detuning, bandwidth and magnitude of random excitation on dynamics of the business cycle system are investigated. The results show that the complex dynamics such as bifurcation, jump domain and so on are induced by time delay and the phenomena that multiple solution or bifurcation is induced by noise. 相似文献
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Stochastic period-doubling bifurcation analysis of a Rssler system with a bounded random parameter
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This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rssler system with an arch-like bounded random parameter. First, we transform the stochastic Rssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic Rssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rssler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rssler system. 相似文献
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研究了时滞及时滞反馈控制参数对Van der Pol系统极限环幅值的影响. 运用自适应的平均场近似方法给出了系统的线性化近似及系统参数Lyapunov稳定性的边界条件, 同时给出了Van der Pol系统的关联时间和功率谱密度的数值模拟结果. 通过与平均场近似下的解析结果比较后发现, 数值模拟结果和理论结果符合.进一步讨论了时滞反馈控制参数、噪声强度以及时滞对关联时间和功率谱密度的影响.
关键词:
平均场近似
关联时间
Lyapunov稳定性 相似文献