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第九届全国动力学与控制学术会议

作者： Shaojuan Ma School of Information & Computation Science North University for Nationalities

orthogonal polynomial approximation is applied to study the stability in a stochastic Logistic system with random *** shows that orthogonal polynomial approximation is effective to reduce the stochastic Logistic system with a random parameter into its equivalent deterministic system,and then the linear stability theory and Jury criterion for nonlinear deterministic discrete systems are applied to the equivalent *** means of the mathematics analysis method we discovered that in stochastic Logistic system when the random intensity and statics parameters of

关键词： Stochastic dynamical system orthogonal polynomial approximation Asymptotic stability

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Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

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Computer Modeling in Engineering & Sciences 2024年第1期138卷 509-524页

作者： Dongmei Huang Dang Hong Wei Li Guidong Yang Vesna Rajic School of Mathematics and Statistics Xidian UniversityXi’an710071China Department of Mathematics Changzhi UniversityChangzhi046011China Department for Statistics and Mathematics Faculty of EconomicsUniversity of BelgradeBelgrade11000Serbia

In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are ***,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state *** condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean ***,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth *** different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic ***,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear ***,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic *** can be found that the excitation frequency can induce period-doubling bifurcation and grazing *** the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change *** is also found that grazing bifurcation appears in advance with increasing of the random *** stronger impulse force can result in the appearance of the diffusion phenomenon.

关键词： orthogonal polynomial approximation vibro-impact systems non-smooth systems grazing bifurcation

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The stability analysis in stochastic Brusselator system with random parameter

The stability analysis in stochastic Brusselator system with...

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第十三届全国非线性振动暨第十届全国非线性动力学和运动稳定性学术会议

作者：马少娟许勇 School of Information & Computation Science Beifang University of Nationalities Department of Applied Mathematics Northwestern Polytechnical University

The stability of Brusselator system with random parameter is explored in this *** the Brusselator system with random parameter can be reduced into the deterministic equivalent system by orthogonal polynomial *** deterministic linear stability theory and the mathematics analysis method are applied to discuss the stability in equivalent *** last the influence of the random parameter on stability in stochastic system is *** is discovered that parameter intervals for asymptotic stability in stochastic Brusselator system is not only related to deterministic parameter,but also to random *** larger the random intensity is,the smaller the parameter interval for asymptotic stability is.

关键词： Stochastic dynamical system orthogonal polynomial approximation Asymptotic stability

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