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	1. Centering Conditions for the Poincar'{e} Systems $P(2,12) $ with a Uniformly Isochronous Center
	XU Jin-Ya, LU Zheng-Yi
	Mathematics 31 December 2014
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	Abstract:We obtain sufficient and necessary centering conditions for the Poincar'e system $P(2,12)$. The necessity of the condition is derived from the first twelve focal values by symbolic computation with Maple, and the sufficiency is proved by verifying the reversibility of the system.
	TO cite this article:XU Jin-Ya, LU Zheng-Yi. Centering Conditions for the Poincar'{e} Systems $P(2,12) $ with a Uniformly Isochronous Center[OL].[31 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4626244


	2. Multiple limit cycles for three-dimensional Lotka-Volterra systems
	LUO Yong, LU Gui-Chen, LU Zheng-Yi
	Mathematics 31 December 2014
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	Abstract:Multiple limit cycles are shown to appear in three-dimensional Lotka-Volterra systems with various types of interactions formed by mutualism, competition and prey-predator. In this paper, under the density dependance and the nonzero off-diagonal elements of interaction matrix, we classify the three-dimensional Lotka-Volterra systems into ten classes and show that besides the known results for classes 2, 3, 5 and 9, in each class of the remaining six ones, a corresponding system can be constructed to have at least two or three limit cycles based on an algorithmic construction method proposed by Hofbauer and So with a modification of Lu and Luo.
	TO cite this article:LUO Yong, LU Gui-Chen, LU Zheng-Yi. Multiple limit cycles for three-dimensional Lotka-Volterra systems[OL].[31 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4626241

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	3. Geometric approach for global asymptotic stability of three species competitive Gompertz models
	LU Gui-Chen, LU Zheng-Yi
	Mathematics 31 December 2014
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	Abstract:This paper deals with the three dimensional competing models with Gompertz growth in biological control, by using the geometric criterion developed by Li and Muldowney and time average property to Gompertz models, some results for the global asymptotical stability of the models are obtained. Furthermore, we have investigated some open problems proposed by Jiang, Niu and Zhu, according to their classification, we have shown that classes 29 and 31 have no periodic orbit, and the interior equilibrium is global asymptotic stability.
	TO cite this article:LU Gui-Chen, LU Zheng-Yi. Geometric approach for global asymptotic stability of three species competitive Gompertz models[OL].[31 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4626235


	4. The Coupling Method and Exponential Decay of Correlations for The Expanding Maps
	WANG Fang
	Mathematics 15 December 2014
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	Abstract:In this article, we consider the standard expanding map $T: mathbb{S}^1 a mathbb{S}^1$ with $T(x)=2xmod 1$. We prove that the correlations of $C^{r}$ observables decay exponentially with the speed $2^{-rn}$, for both $r in (0,1)$ and $rinZ^+$. The main tool we are using in this work is the coupling method. We remark that our result can be easily extended to general expanding map $T(x)=mxmod 1$, $orall min mathbb{Z}^+$.
	TO cite this article:WANG Fang. The Coupling Method and Exponential Decay of Correlations for The Expanding Maps[OL].[15 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4623829


	5. Hamiltonian Systems with Positive Topological Entropy and Conjugate Points
	LIU Fei, WANG Zhiyu, WANG Fang
	Mathematics 30 November 2014
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	Abstract:In this article, we consider the natural Hamiltonian systems $H(x,p)=rac{1}{2}g^{ij}(x)p_{i}p_{j}+V(x)$ defined on a smooth Riemannian manifold $(M = S^{1} imes N, g)$, where $S^{1}$ is the one dimensional torus, $N$ is a compact manifold, $g$ is the Riemannian metric on $M$ and $V$ is a potential function satisfying $V leq 0$. We prove that under suitable conditions, if the system has positive topological entropy and the fundamental group $pi_{1}(N)$ has sub-exponential growth rate, then the Riemannian manifold $M$ with the Jacobi metric $(h-V)g$, i.e., $(M, (h-V)g)$, is a manifold with conjugate points for all $h$ with $0 < h <delta$, where $delta$ is a small number.
	TO cite this article:LIU Fei, WANG Zhiyu, WANG Fang. Hamiltonian Systems with Positive Topological Entropy and Conjugate Points[OL].[30 November 2014] http://en.paper.edu.cn/en_releasepaper/content/4621077


	6. Computer Aided Proof for the Global Stability of a Lotka-Volterra System with Discrete Diffusions
	YANG Ming, LU Zheng-Yi
	Mathematics 01 November 2014
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	Abstract:In this paper, based on the PD algorithm and the computer system Maple, the Hofbauer-So-Takeuchi conjecture for a Lotka-Volterra system with discrete diffusion is proved in the case of $n = 5$ by checking the positive definiteness of a class of polynomials with the largest one 4874376 terms.
	TO cite this article:YANG Ming, LU Zheng-Yi. Computer Aided Proof for the Global Stability of a Lotka-Volterra System with Discrete Diffusions[OL].[ 1 November 2014] http://en.paper.edu.cn/en_releasepaper/content/4616114


	7. On soliton solutions of a class of discrete Schr
	Liu Chungen, Zhen Youquan
	Mathematics 06 March 2014
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	Abstract:In this paper, we consider a class of discrete Schr"{o}dinger system. We divide the discussion into two cases. In the first case, we consider the system with unbounded potential. The existence of a nontrivial solution with both of the two components are nonzero is obtained. In the second case, we consider the system with radially symmetric coefficients and find radially symmetric solutions. After proving a compactness result we prove the existence of a nontrivial radially symmetric solution.
	TO cite this article:Liu Chungen, Zhen Youquan. On soliton solutions of a class of discrete Schr[OL].[ 6 March 2014] http://en.paper.edu.cn/en_releasepaper/content/4588978


	8. Modeling the dynamics of epidemic spreading on homogenousand heterogeneous networks
	Yao Hu,Lequan Min,Yang Kuang
	Mathematics 03 January 2014
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	Abstract:This paper proposes two modifiedsusceptible-infected-recovered-susceptible (SIRS) models onhomogenous and heterogeneous networks, respectively. In the study ofthe homogenous network model, it is proved that if the basicreproduction number $R_0$ of the model is less than one, then thedisease-free equilibrium is locally asymptotically stable andbecomes globally asymptotically stable under the condition that thethreshold value $R_1$ is less than one. Otherwise, if $R_0$ is morethan one, the endemic equilibrium is locally asymptotically stableand becomes globally asymptotically stable under the assume that thetotal population $N $ will tend to a specific plane. In the study ofthe heterogeneous network model, this paper discusses the existencesof the disease-free equilibrium and endemic equilibrium of themodel. It is proved that if the threshold value $ ilde{R}_0$ isless than one, then the disease-free equilibrium is globallyasymptotically stable. Otherwise, if $ ilde{R}_0$ is more than one,the system is permanent. A series of numerical experiments are givento illustrate the theoretical results. We also numerically predictthe effect of vaccination ratio on the size of HBV infected mainlandChinese population.
	TO cite this article:Yao Hu,Lequan Min,Yang Kuang. Modeling the dynamics of epidemic spreading on homogenousand heterogeneous networks[OL].[ 3 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4580447


	9. On the dominated splittings of the tangent flow
	YANG Da-Wei
	Mathematics 23 December 2013
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	Abstract:A smooth vector field will generate a smooth flow. The linearization of the flow with respect to the space variable is called the tangent flow. For an invariant set, one can define the hyperbolic splitting, the partially hyperbolic splitting and the dominated splitting of the tangent flow. We will prove that under some condition, i.e., the set is a weekly transitive set, and the set contains only hyperbolic singularities, then the dominated splitting of the tangent flow on the set implies the partially hyperbolic splitting.
	TO cite this article:YANG Da-Wei. On the dominated splittings of the tangent flow[OL].[23 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4577826


	10. On the strong stable manifold of singularities in a non-trivial Lyapunov stable chain recurrent class
	YANG Da-Wei
	Mathematics 23 December 2013
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	Abstract:In the research of Palis conjecture, one is interesting with some Lyapunov stable chain recurrent classes. For the case of vector fields, we would like to study the properties of some singularity which is contained in a Lyapunov stable chain recurrent class. We prove that for a generic vector field which is far away from homoclinic tangencies, if a singularity is contained in a non-trivial Lyapunov stable chain recurrent class, then the singularity has some strong stable manifold, which intersects the chain recurrent class only at the singularity.
	TO cite this article:YANG Da-Wei. On the strong stable manifold of singularities in a non-trivial Lyapunov stable chain recurrent class[OL].[23 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4577820

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