The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itô differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species.
The principal resonance of Duffing oscillator to combined deterministic and random external excitation was investigated. The random excitation was taken to be white noise or harmonic with separable random amplitude and phase. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method. These two one-peak-density functions were combined using the probability of realization of the two stable stationary solutions to obtain the double peak probability density function. The theoretical analysis are verified by numerical results.
This paper gives the direct formulas of stiffness matrixes of two'kinds of Kirchboff nonlinear elements under total-Lagrangecoordinate. For the first one, it includes not only the quadric terms of increments of strain and displacegnent but aiso.th e influence of rotations. For the second one, it is simpllfied ~ut its nonlinear ts cor~idered by taking into account the influence of axial force on the equilibrium equation in the litwar beam .theory. The nonlinear equation obtained from both of the above,said elements is SOlved by mixed Newton-Raphson method, and by comparing the results obtained from two kinds of nonlinear beam some important conclusions that we can know how to use them right are given in our paper.
This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rössler system with an arch-like bounded random parameter. First, we transform the stochastic Rössler 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 Rössler 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 Rössler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rössler system.
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