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	1. Eco-evolutionary dynamics with feedback driven by imitation
	Cao Lixuan,Bin Wu
	Mathematics 12 March 2021
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	Abstract:Eco-evolutionary dynamics with environmental feedback occur when individual action modifies both the relative abundance of strategies and surrounding environment. The feedback mechanism can be captured by a function from actions of the population to the environment. As for the evolution of strategies, replicator equation common models it based on the natural selection. However, strategies spread not only by natural selection but also by imitation in evolutionary game. Specifically, Fermi process, as a kind of imitation rule, is generally adopted by individuals. This work propose a class of ecoevolutionary dynamics where strategies coevolve with the environment by general imitation functions. Then the condition under which a limit cycle may occur in the system is obtained, which can never be present in coupled replicator dynamics with environment. Further, the dynamical outcomes can be devided into four cases and compare with the classical system in detail.
	TO cite this article:Cao Lixuan,Bin Wu. Eco-evolutionary dynamics with feedback driven by imitation[OL].[12 March 2021] http://en.paper.edu.cn/en_releasepaper/content/4754090


	2. Chaos and control of a generalized higher-order nonlinearSchr
	Li Min, Lei Wang, Feng-HuaQi
	Mathematics 25 August 2015
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	Abstract:The nonlinear dynamics of a generalized higher-ordernonlinear Schr"{o}dinger (HNLS) equation with a periodic externalperturbation is investigated numerically. Via the phase planeanalysis, it's found that both the homoclinic orbits andheteroclinic orbits can exist for the unperturbed HNLS equationunder certain conditions. Moreover, under the effect of the periodicexternal perturbation, the quasi-periodic bifurcations arise and canevolve into the chaos. The dynamical responses of the perturbed HNLSequation with regard to the perturbation strength are simulatedthrough the bifurcation diagrams, maximum Lyapunov exponents andphase portraits, which further prove the existence of the chaos forthe HNLS equation with a periodic external perturbation.Furthermore, two methods are used to control the chaos effectively,which can make the chaotic motions evolve into the stablequasi-periodic orbits. Those studies are helpful to reveal thedynamical properties of the HNLS equation.
	TO cite this article:Li Min, Lei Wang, Feng-HuaQi. Chaos and control of a generalized higher-order nonlinearSchr[OL].[25 August 2015] http://en.paper.edu.cn/en_releasepaper/content/4653119


	3. 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


	4. Quasi-periodic Solutions of Completely Resonant Forced Beam Equations
	Gao Yixian,Chen Bochao
	Mathematics 21 October 2013
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	Abstract:This paper is concerned with the existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear beam equations subject to periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number. The proofs are based on the variational Lyapunov-Schmidt reduction and the linking theorem.
	TO cite this article:Gao Yixian,Chen Bochao. Quasi-periodic Solutions of Completely Resonant Forced Beam Equations[OL].[21 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4565116


	5. Centers and bifurcations of a switching quadratic system
	CHEN Xingwu
	Mathematics 18 March 2011
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	Abstract:In this paper we study the center problem and the limit cycle bifurcation of switching differential systems. Computing the generalized Lyapunov constants and decomposing their variety, we obtain the center condition of a switching quadratic system. Moreover, developing Christopher's method of finding limit cycles near centers for analytic systems, we prove that there are perturbations having 9 limit cycles near the center at the origin of the considered switching quadratic system.
	TO cite this article:CHEN Xingwu. Centers and bifurcations of a switching quadratic system[OL].[18 March 2011] http://en.paper.edu.cn/en_releasepaper/content/4417051


	6. Infinitely many solutions for an elliptic system
	Lihong Huang,Ronghui Hu
	Mathematics 31 March 2008
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	Abstract:By using the generalized symmetric mountain pass theorem developed by Bartsch and Clapp through the limit relative category of Fournier et al, we prove the existence of infinitely many solutions for an elliptic system with Dirichlet boundary conditions. Some existing results are extended.
	TO cite this article:Lihong Huang,Ronghui Hu. Infinitely many solutions for an elliptic system[OL].[31 March 2008] http://en.paper.edu.cn/en_releasepaper/content/19955


	7. Nonexistence of formal first integrals for general nonlinear systems under resonance
	Fang Liu,Shaoyun Shi,Zhiguo Xu
	Mathematics 19 December 2007
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	Abstract:In the present paper, we consider the non-integrability for nonlinear system under the simple resonant case, i.e., the Jacobian matrix of vector field at some fixed point has some single multiply zero eigenvalues, and some nonzero eigenvalues which are $\\\\\\\\\\\\\\\\mathbb{N}$-independent. By using normal form theory, we give a necessary condition for this kind of system to have formal first integral.
	TO cite this article:Fang Liu,Shaoyun Shi,Zhiguo Xu. Nonexistence of formal first integrals for general nonlinear systems under resonance[OL].[19 December 2007] http://en.paper.edu.cn/en_releasepaper/content/17140

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