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	1. Measure-theoretic Entropy for Weak-solvable Cancellative Left-amenable Semigroup
	HUANG ShiYao,HUANG XiaoJun
	Mathematics 16 March 2023
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	Abstract:The study of dynamical systems under semigroup actions is an important branch of topological dynamical systems. At the same time, the study of dynamical system entropy is also of great significance, among which metric entropy can measure the complexity of the motion of a dynamical system on a probability space and constitutes an invariant of isomorphic systems. The main research content of this article is to generalize the Fekete lemma to weakly solvable cancellative conformal semigroups, and prove that the limit related to the F$\phi$lner sequence in this semigroup satisfies the "infimum rule". Finally, the metric entropy of the dynamical system under this semigroup action is given.
	TO cite this article:HUANG ShiYao,HUANG XiaoJun. Measure-theoretic Entropy for Weak-solvable Cancellative Left-amenable Semigroup[OL].[16 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759489


	2. On the limit quasi-shadowing property
	Fang Zhang, Yunhua Zhou
	Mathematics 10 April 2015
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	Abstract:The paper study the limit quasi-shadowing property for diffeomorphisms.This paper prove that any quasi-partially hyperbolic pseudoorbit ${x_{i},n_{i}}_{iin mathbb{Z}}$ can be $mathcal{L}^p$-, limit and asymptotic quasi-shadowed by a points sequence ${y_{k}}_{kin mathbb{Z}}$.Moreover, this paper also investigate the $mathcal{L}^p$-, limit and asymptotic quasi-shadowing properties for partially hyperbolic diffeomorphisms which are dynamically coherent.
	TO cite this article:Fang Zhang, Yunhua Zhou. On the limit quasi-shadowing property[OL].[10 April 2015] http://en.paper.edu.cn/en_releasepaper/content/4638485


	3. 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


	4. Chaos in nonautonomous discrete dynamical systems approached by their subsystems
	SHI Yuming
	Mathematics 17 April 2012
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	Abstract:A nonautonomous discrete dynamical systemis generated by a given sequence of maps. A new type of subsystem of it isintroduced. It is generated by a sequence of mapsthat are partial compositions of the given sequence of maps in the original orderso that every orbit of the subsystem is a part of anorbit of the original system starting from a same initial point.A concept of chaos in the strong sense of Wiggins is introduced.Some close relationships between chaotic dynamical behaviorsof the original system and its subsystems are given, includingchaos in the (strong) sense of Li-Yorke and Wiggins.By applying these relationships, several criteria of chaos are establishedand some sufficient conditions for no chaos are given for nonautonomous discrete systems.
	TO cite this article:SHI Yuming. Chaos in nonautonomous discrete dynamical systems approached by their subsystems[OL].[17 April 2012] http://en.paper.edu.cn/en_releasepaper/content/4475266


	5. New Periodic Solutions for the Circular Restricted 3-Body and 4-Body Problems
	Zhang Shiqing,Yin Qunyao
	Mathematics 24 February 2009
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	Abstract:For the circular restricted 3-body and 4-body problems in R^2, we prove the existence of new symmetric noncollision periodic solutions with some fixed winding numbers and masses.Our results should be useful in celestial mechanics.
	TO cite this article:Zhang Shiqing,Yin Qunyao. New Periodic Solutions for the Circular Restricted 3-Body and 4-Body Problems[OL].[24 February 2009] http://en.paper.edu.cn/en_releasepaper/content/29566


	6. Generalizations on Rabinowitz’s Theorems
	Zhang Shiqing
	Mathematics 20 February 2009
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	Abstract:We use the famous Benci-Rabinowitz’s Saddle Point Theorem ([3])with Cerami-Palais-Smale condition to study the existence of new periodic solutions with a fixed period for second order Hamiltonian systems under weaker conditions than Rabinowitz’s original conditions in his pioneer paper([11]),the key point of our proof is proving Cerami-Palais-Smale condition,which is difficult since no symmetry for the potential. We use Rabinowitz’s Saddle Point Theorem to study periodic solution for sub-quadratic second order Hamiltonian systems.
	TO cite this article:Zhang Shiqing. Generalizations on Rabinowitz’s Theorems[OL].[20 February 2009] http://en.paper.edu.cn/en_releasepaper/content/29417


	7. Effect of prey refuge on the dynamics and equilibrium density of
	Ma Zhihui ,Li Zizhen ,Wang Shufang
	Mathematics 30 October 2007
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	Abstract:In this paper, we use an analytical approach to study the dynamics of the simplest forms of refuge using by prey. Here we incorporate prey refuge in a widely known continuous model\|the Lotka-Volterra model. We will evaluate the effect of prey refuge with regard to the local stability of equilibrium points in the 痳st quadrant and equilibrium density values. The results show that the effect of prey refuge can enhance the stability of equilibrium points and equilibrium density of prey and predator populations.
	TO cite this article:Ma Zhihui ,Li Zizhen ,Wang Shufang . Effect of prey refuge on the dynamics and equilibrium density of[OL].[30 October 2007] http://en.paper.edu.cn/en_releasepaper/content/16034

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