Abstract:In multi-species population, the extinction event is one of the most important phenomena during the evolution of the population.The fate of one species not only determined by itself, but also influenced by other species with which it interacts.Therefore, the extinction of one species has huge influenced on the whole population.Previous researches shows how randomness affects the extinction time of finite population by simulation.However, the mathematical analysis of extinction time is absent.Here we investigate the extinction time under the finite population which adopts the cyclic Rock-Paper-Scissors game.We find a solution of extinction time based on stochastic process under neutral drift.Then for the situation that selection intensity is not vanishing, we get a partial differential equation (PDE) to depict the extinction time.We analyse the PDE under weak selection intensity.Moreover, although our research starts from the model adopting the Fermi process, and we proved that the extinction time under the general imitation process can be known based on our results of the Fermi process.

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	1. Extinction Time Analysis under cyclic-dominant stochastic population
	ZHANG Li-Bin, WU Bin
	Mathematics 19 March 2021
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (153K B)

	Abstract:In multi-species population, the extinction event is one of the most important phenomena during the evolution of the population.The fate of one species not only determined by itself, but also influenced by other species with which it interacts.Therefore, the extinction of one species has huge influenced on the whole population.Previous researches shows how randomness affects the extinction time of finite population by simulation.However, the mathematical analysis of extinction time is absent.Here we investigate the extinction time under the finite population which adopts the cyclic Rock-Paper-Scissors game.We find a solution of extinction time based on stochastic process under neutral drift.Then for the situation that selection intensity is not vanishing, we get a partial differential equation (PDE) to depict the extinction time.We analyse the PDE under weak selection intensity.Moreover, although our research starts from the model adopting the Fermi process, and we proved that the extinction time under the general imitation process can be known based on our results of the Fermi process.
	TO cite this article:ZHANG Li-Bin, WU Bin. Extinction Time Analysis under cyclic-dominant stochastic population[OL].[19 March 2021] http://en.paper.edu.cn/en_releasepaper/content/4754233


	2. 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


	3. Finite-time Synchronization for coupled nonidentical Duffing-type oscillatordynamical networks
	LV Mengting,ZHANG Zhengqiu,REN Ling
	Mathematics 08 March 2021
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	Abstract:In this paper, the finite-time synchronization for a class of coupled nonidentical drive-response Duffing-type oscillator dynamical networks is studied. using differential analytical techniques from exisiting papers, and establishing driving response system model of coupling Duffing dynamic network . Then the error system was obtained by transforming the driving response system and designed a reasonable controller , two novel conditions toassure the finite-time synchronization for above networks are acquired by combining integral inequality skills with transforming two differential inequalities into a differential inequality. Based on the results given in this paper, two examples are listed, which implies the validity of these conditions Meanwhile, getting rid of utilizing the finite-time synchronization theorems, our study work widens the research method of the finite-time synchronization for dynamical networks.
	TO cite this article:LV Mengting,ZHANG Zhengqiu,REN Ling. Finite-time Synchronization for coupled nonidentical Duffing-type oscillatordynamical networks[OL].[ 8 March 2021] http://en.paper.edu.cn/en_releasepaper/content/4753943


	4. Ground state solution for Schr\"{o}dinger-KdV system with asymptotically periodic potential
	Liang Fei-Fei,Wu Xing-Ping,Tang Chun-Lei
	Mathematics 08 March 2021
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	Abstract:In this paper, we study the coupled nonlinear Schr\"{o}dinger-Korteweg-de Vries system with asymptotically periodic potential. By using the variational method and Nehari manifold, we obtain the existence of non-trivial ground state solution in dimensions $N\leq3$.
	TO cite this article:Liang Fei-Fei,Wu Xing-Ping,Tang Chun-Lei. Ground state solution for Schr\"{o}dinger-KdV system with asymptotically periodic potential[OL].[ 8 March 2021] http://en.paper.edu.cn/en_releasepaper/content/4753986


	5. Positive solutions for coupled system of nonlinear fractional differential equations with nonlocal conditions
	QI Chao-Fan,XUE Chun-Yan
	Mathematics 22 February 2021
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	Abstract:In this work, we study the existence of positive solutions for a nonlinear coupled system of Riemann-Liouville derivatives fractional differential equations with integral boundary value problems and a parameter. By means of a new fixed point theory due to Radu Precup, Krasnoselskii's cone fixed point theory of the vector version, we also investigate the localization and multiplicity of the positive solutions.
	TO cite this article:QI Chao-Fan,XUE Chun-Yan. Positive solutions for coupled system of nonlinear fractional differential equations with nonlocal conditions[OL].[22 February 2021] http://en.paper.edu.cn/en_releasepaper/content/4753658


	6. Existence and concentration of ground state solutions for Chern-Simons-Schr\"{o}dinger systems with steep well potential
	Jin-Lan Tan,Yong-Yong Li,Chun-Lei Tang
	Mathematics 03 February 2021
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	Abstract:In this paper, we investigate a class of nonlinear Chern-Simons-Schr\"{o}dinger system with steep well potential.\ By using the variational methods,\ the mountain pass theorem and the Nehari manifold methods,\ we prove the existence of ground state solutions for $\lambda>0$ large enough.\ Furthermore,\ we verify the asymptotic behavior of ground state solutions as $\lambda\to+\infty$.
	TO cite this article:Jin-Lan Tan,Yong-Yong Li,Chun-Lei Tang. Existence and concentration of ground state solutions for Chern-Simons-Schr\"{o}dinger systems with steep well potential[OL].[ 3 February 2021] http://en.paper.edu.cn/en_releasepaper/content/4753525


	7. Results on Solution Continuity for Unified Set-valued Vector Equilibrium Problems
	Ye XiuLian,CHEN Chun-Rong,CHEN Chun-Rong
	Mathematics 12 January 2021
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	Abstract:The stability analysis of unified set-valued vector equilibrium problems via improvement sets is discussed in this paper. First, we obtain the linear scalarization characterizations to solutions for unified weak set-valued vector equilibrium problems and to $E$-Benson proper efficient solutions for unified set-valued vector equilibrium problems. Then, by the linear scalarization characterizations, the solution continuity and the $E$-Benson proper efficient solution continuity for parametric unified weak set-valued vector equilibrium problems and parametric unified set-valued vector equilibrium problems are established, respectively.
	TO cite this article:Ye XiuLian,CHEN Chun-Rong,CHEN Chun-Rong. Results on Solution Continuity for Unified Set-valued Vector Equilibrium Problems[OL].[12 January 2021] http://en.paper.edu.cn/en_releasepaper/content/4753460


	8. Existence and concentration of semi-classical ground state solutions for Chern-Simons-Schr\"{o}dinger system
	Wang Linjing,Li Guidong,Tang Chun-Lei
	Mathematics 05 January 2021
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	Abstract:In this paper, we study the equation\begin{equation} -\varepsilon^{2}\Delta u+ V(x)u+\left(A_{0}(u)+A_{1}^{2}(u)+A_{2}^{2}(u)\right)u=f(u) \ \ \ \ \mathrm{in} ~ H^{1}(\mathbb{R}^{2}),\end{equation}where $\varepsilon$ is a small parameter, $V$ is the external potential,$A_i(i=0,1,2)$ is the gauge field and $f\in C(\mathbb{R}, \mathbb{R})$ is 5-superlinear growth.By using variational methods and analytic technique, we prove that this system possesses a ground state solution $u_\varepsilon$.Moreover, our results show that, as $\varepsilon\to 0$, the global maximum point $x_\varepsilon$ of $u_\varepsilon$ must concentrate at the global minimum point $x_0$ of $V$.
	TO cite this article:Wang Linjing,Li Guidong,Tang Chun-Lei. Existence and concentration of semi-classical ground state solutions for Chern-Simons-Schr\"{o}dinger system[OL].[ 5 January 2021] http://en.paper.edu.cn/en_releasepaper/content/4753373


	9. Optimizes a convex function on a multi-objective efficient set
	Wang Ting,Yao Bin
	Mathematics 03 December 2020
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	Abstract:The optimization problem of convex function on effective set of multi-objective optimizationhas many useful applications in multi-criteria decision making. In mathematics, problem (P) can be classified as a global optimization problem.This type of problem is more difficult to solve than convex programming problems.In this paper, penalty function method and parameter method for global optimal solution are proposed, and the cases with equality constraint are discussed.
	TO cite this article:Wang Ting,Yao Bin. Optimizes a convex function on a multi-objective efficient set[OL].[ 3 December 2020] http://en.paper.edu.cn/en_releasepaper/content/4753148


	10. Theory of scissor products and applications
	ZHU Yong-Wen
	Mathematics 18 November 2020
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