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The first-passage problem is an important issue in the theory of dynamical systems; it determines whether the system is safe and reliable or destroyed. Therefore, taking a suitable force to control first-passage failure is very significant for such systems. In this paper, we study the reliability of a stochastically complex dynamical system by using the stochastic averaging method. The reliability results show that the reliability function is monotonically decreasing with respect to time, and that the reliability of the system is relatively worse, with external and parametric white-noise excitations. A bang–bang feedback control is used to improve the reliability for the original system. Numerical results display that even a small control force can greatly enhance the reliability of the original system.  相似文献   
2.
Jiaorui Li  C.S. Feng 《Physica A》2010,389(24):5557-5562
First-passage failure of a classical business cycle model subject to time-delayed feedback control and wide-band random excitation is investigated in this paper. First, we get the averaged equation by using a stochastic averaging method, and then a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. The conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations analytically and numerically with suitable initial and boundary conditions. The results show that time delay in the feedback control forces may remarkably reduce the conditional reliability and the mean first-passage time of the controlled economics system.  相似文献   
3.
Chaos prediction and its control of the Goodwin model under the deterministic or stochastic excitation are studied theoretically and numerically. Applying the Melnikov technique, the threshold conditions for the occurrence of chaos are obtained theoretically. The stable and unstable manifolds of saddle are computed to verify the effectiveness of the analytical prediction in the deterministic case. Also, the safe basins are introduced to show how the externally stochastic perturbation affects the safety of the economic system as the noise amplitude increases. Finally, the analytical criterion of controlling chaos is derived via the delayed feedback control method. Numerical investigations including the top Lyapunov exponent, Poincare section, and phase portraits are carried out to demonstrate the validity and effectiveness of the theoretical results.  相似文献   
4.
Stochastic stabilization of first-passage failure of Rayleigh oscillator under Gaussian White-Noise parametric excitation is studied. The equation of motion of the system is first reduced to an averaged Itô stochastic differential equation by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function of first-passage failure is established. The conditional reliability function, and the conditional probability density are obtained by solving the backward Kolmogorov equation with boundary conditions. Finally, the cost function and optimal control forces are determined by the requirements of stabilizing the system by evaluating the maximal Lyapunov exponent. The numerical results show that the procedure is effective and efficiency.  相似文献   
5.
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Itô stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.  相似文献   
6.
Jiaorui Li  Zhengzheng Ren 《Physica A》2008,387(23):5844-5851
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   
7.
The chaotic behavior of Van der Pol–Mathieu–Duffing oscillator under bounded noise is investigated. By using random Melnikov technique, a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system. The results show that the threshold of bounded noise amplitude for the onset of chaos in this system increases as the intensity of the noise in frequency increases, which is further verified by the maximal Lyapunov exponents of the system. The effect of bounded noise on Poincaré map is also investigated, in addition the numerical simulation of the maximal Lyapunov exponents.  相似文献   
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