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ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS

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Journal of Systems Science & Complexity 2008年第1期21卷 119-128页

作者： jiaqi mo Wantao LIN Department of Mathematics Anhui Normal University Wuhu 241000 China Division of Computational Science E-Institutes of Shanghai Universities at SJTU Shanghai 200240 China. LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China.

A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.

关键词： Activator system nonlinear reaction diffusion singular perturbation.

GENERALIZED VARIATION ITERATION SOLUTION OF AN ATmoSPHERE-OCEAN OSCILLATOR moDEL FOR GLOBAL CLIMATE

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Journal of Systems Science & Complexity 2011年第2期24卷 271-276页

作者： jiaqi mo Wantao LIN Anhui Normal University Wuhu 241000 China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong University Shanghai 200240 China State Key Laboratory of Numerical modeling for Atmospheric Sciences and Geophysical Fluid Dynamic Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China

A box model of the interhemispheric thermohaline circulation （THC） in atmosphere-ocean for global climate is considered. By using the generalized variational iteration method, the approximate solution of a simplified nonlinear model is studied. The generalized variational iteration method is an analytic method, and the obtained analytic solution can be operated sequentially. The authors also diversify qualitative and quantitative behaviors for corresponding physical quantities.

关键词： Approximate solution atmosphere-ocean E1 Nino-Southern oscillation variational iteration.

A class of epidemic virus transmission population dynamic system

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维普期刊数据库

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Applied Mathematics and Mechanics(English Edition) 2017年第8期38卷 1181-1190页

作者： Cheng OUYANG Min ZHU jiaqi mo Faculty of Science Huzhou UniversityHuzhou 313000Zhejiang ProvinceChina School of Mathematics and Computer Science Anhui Normal UniversityWuhu 241003Anhui ProvinceChina

A class of epidemic virus transmission population dynamic system is considered. Firstly, using the functional homotopic analysis method, an initial approximate function is selected. Then, the arbitrary order approximate analytic solutions are obtained successively. Finally, the accuracy of the obtained approximate analytic solutions is described. The influence of the various physical parameters for the epidemic virus transmission population dynamic system is discussed.

关键词： epidemic approximate analytic successively perturbation arbitrary qualitative asymptotic attractive manifold

THE SINGULARLY PERTURBED NONLOCAL BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER NONLINEAR ELLIPTIC EQUATIONS

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Applied Mathematics(A Journal of Chinese Universities) 1998年第1期13卷 1-7页

作者： mo jiaqi Department of Mathematics Anhui Normal University Wuhu 241000 China

In this paper,a class of singular perturbation of nonlocal boundary value problems for elliptic partial differential equations of higher order is considered by using the differential *** uniformly valid asymptotic exp... 详细信息

关键词： Differential inequality singular perturbation asymptotic expansion elliptic differential equation nonlocal boundary value problem.

A SINGULARLY PERTURBED PROBLEM FOR STABLE SUPERSONIC FLOW

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Applied Mathematics(A Journal of Chinese Universities) 1999年第2期14卷 153-157页

作者： mo jiaqi Dept. of Math. Anhui Normal Univ. Wuhu

In this paper,a singularly perturbed problem for the stable fluid flow is *** supersonic speed at upper reaches and subsonic speed at lower reaches in a duct,the position of shock layer is analyzed and the asymptotic ... 详细信息

关键词： 1991 MR Subject Classification 34E15 34A40

Approximate Solution for Mechanism of Thermally and Wind-driven Ocean Circulation

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Chinese Geographical Science 2010年第5期20卷 383-388页

作者： mo jiaqi LIN Wantao LIN Yihua Anhui Normal University Wuhu 241000 China State Key Laboratory of Numerial modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Division of Computational Science E-Institutes of Shanghai Universities at Shanghai Jiaotong University Shanghai 200240 China

The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.

关键词： global climate atmosphere-ocean oscillation homotopic mapping approximate solution

SINGULARLY PERTURBED SOLUTION FOR THIRD ORDER NONLINEAR EQUATIONS WITH TWO PARAMETERS

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Analysis in Theory and Applications 2007年第4期23卷 301-306页

作者： jiaqi mo Anhui Normal University China E-Institutes of Shanghai Universities at SJTU China Huzhou Teachers College China

A class of singularly perturbed boundary value problems for nonlinear equation of the third order with two parameters is considered. Under suitable conditions, using the theory of differential inequalities the existen... 详细信息

关键词： nonlinear two parameters singular perturbation

Singularly Perturbed Solution of Coupled model in Atmosphere-ocean for Global Climate

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Chinese Geographical Science 2008年第2期18卷 193-196页

作者： mo jiaqi LIN Wantao WANG Hui Department of Mathematics Anhui Normal University Wuhu 241000 China Division of Computational Science E-Institutes of Shanghai Universities at SJTU Shanghai 200240 China Huzhou Teachers College Huzhou 313000 China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Chinese Academy ofMeteorological Sciences Beijing 100081 China

A box model of the interhemispheric thermohaline circulation (THC) in atmosphere-ocean for global cli-mate is considered. By using the multi-scales method, the asymptotic solution of a simplified weakly nonlinear model is discussed. Firstly, by introducing first scale, the zeroth order approximate solution of the model is obtained. Sec-ondly, by using the multi-scales, the first order approximate equation of the model is found. Finally, second order ap-proximate equation is formed to eliminate the secular terms, and a uniformly valid asymptotic expansion of solution is decided. The multi-scales solving method is an analytic method which can be used to analyze operation sequentially. And then we can also study the diversified qualitative and quantitative behaviors for corresponding physical quantities. This paper aims at providing a valid method for solving a box model of the nonlinear equation.

关键词： atmosphere-ocean El Nino-Southern Oscillation singular perturbation approximate solution

Homotopic Mapping Solving Method for Perturbed Mechanism of Western Boundary Undercurrents in Equator Pacific

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Chinese Geographical Science 2006年第4期16卷 347-350页

作者： mo jiaqi WANG Hui LIN Wantao Department of Mathematics Anhui Normal University Wuhu 241000 China Division of Computational Science E-Instilutes of Shanghai Universities Shanghai Jiaotong University Shanghai 200240 China Department of Mathematics Huzhou Teachers College Huzhou 313000 China Chinese Academy of Meteorological Sciences Beijing 100081 China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China

The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment, but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-eogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value. It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.

关键词： undercurrent perturbation approximate solution equator Pacific