In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in...In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.展开更多
本文研究了移动环境下一类具有时滞的Lotka-Volterra合作系统行波解的存在性。利用单调迭代方法,通过构造合适的上下解,证明了当环境运动速度c>max{ c1∗,c2∗}时,系统连接两边界平衡点的行波解的存在性。Existence of traveling wave ...本文研究了移动环境下一类具有时滞的Lotka-Volterra合作系统行波解的存在性。利用单调迭代方法,通过构造合适的上下解,证明了当环境运动速度c>max{ c1∗,c2∗}时,系统连接两边界平衡点的行波解的存在性。Existence of traveling wave front solutions is established for diffusive and cooperative Lotka-Volterra system with delays in a shifting environment. Using the method of monotone iteration and by constructing appropriate upper and lower solutions, it is proven that when the environmental movement speed is c>max{ c1∗,c2∗}, there exist traveling wave solutions that connect the boundary equilibrium points of the system.展开更多
考虑在移动环境下局部扩散三种群Lotka-Volterra竞争合作系统行波解的存在性,并假设此系统的内禀增长率函数恒大于某正常数。通过构造一对有序的上下解并利用单调迭代技巧和波动引理,证明了系统的非负受迫行波的存在性。We consider the...考虑在移动环境下局部扩散三种群Lotka-Volterra竞争合作系统行波解的存在性,并假设此系统的内禀增长率函数恒大于某正常数。通过构造一对有序的上下解并利用单调迭代技巧和波动引理,证明了系统的非负受迫行波的存在性。We consider the existence of traveling wave solutions for Lotka-Volterra competitive-cooperative system with three-species under a shifting habitat, and assume that the intrinsic growth rate functions of this system are greater than the normal numbers. We prove the existence of non-negative forced traveling waves of the system by constructing a pair of upper and lower solutions and using monotonic iterative techniques and the fluctuation lemma.展开更多
为了描述移动环境轻度恶化对两个弱合作物种的持久性产生的影响,本文考虑一类带有与时空均相关的恒正内禀增长函数的格上Lotka-Volterra合作系统。通过构造合适的上下解并结合单调迭代的方法证明了系统存在两组受迫行波解。In order to ...为了描述移动环境轻度恶化对两个弱合作物种的持久性产生的影响,本文考虑一类带有与时空均相关的恒正内禀增长函数的格上Lotka-Volterra合作系统。通过构造合适的上下解并结合单调迭代的方法证明了系统存在两组受迫行波解。In order to characterize the effect of mild deterioration of the shifting environment on the two weakly cooperative species persistence, we consider a class of the lattice Lotka-Volterra cooperative systems with a constant positive intrinsic growth function that is spatio-temporally correlated. By constructing suitable upper and slower solutions combined with the method of monotone iteration, we prove that there exist two sets of forced traveling wave solutions for the system.展开更多
This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal(convolution)dispersals:{u_(t)=k*u-u+u(1-u-av),x∈R,t∈R,vt=d(k*v-v)+rv(1-v-bu),c∈R,t∈...This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal(convolution)dispersals:{u_(t)=k*u-u+u(1-u-av),x∈R,t∈R,vt=d(k*v-v)+rv(1-v-bu),c∈R,t∈R.(0.1)Here a≠1,b≠1,d,and r are positive constants.By studying the eigenvalue problem of(0.1)linearized at(ϕc(ξ),0),we construct a pair of super-and sub-solutions for(0.1),and then establish the existence of entire solutions originating from(ϕc(ξ),0)as t→−∞,whereϕc denotes the traveling wave solution of the nonlocal Fisher-KPP equation ut=k*u−u+u(1−u).Moreover,we give a detailed description on the long-time behavior of such entire solutions as t→∞.Compared to the known works on the Lotka-Volterra competition system with classical diffusions,this paper overcomes many difficulties due to the appearance of nonlocal dispersal operators.展开更多
Gyllenberg and Yan(Discrete Contin Dyn Syst Ser B 11(2):347–352,2009)presented a system in Zeeman’s class 30 of 3-dimensional Lotka-Volterra(3D LV)competitive systems to admit at least two limit cycles,one of which ...Gyllenberg and Yan(Discrete Contin Dyn Syst Ser B 11(2):347–352,2009)presented a system in Zeeman’s class 30 of 3-dimensional Lotka-Volterra(3D LV)competitive systems to admit at least two limit cycles,one of which is generated by the Hopf bifurcation and the other is obtained by the Poincaré-Bendixson theorem.Yu et al.(J Math Anal Appl 436:521–555,2016,Sect.3.4)recalculated the first Liapunov coefficient of Gyllenberg and Yan’s system to be positive,rather than negative as in Gyllenberg and Yan(2009),and pointed out that the Poincaré-Bendixson theorem is not applicable for that system.Jiang et al.(J Differ Equ 284:183–218,2021,p.213)proposed an open question:“whether Zeeman’s class 30 can be rigorously proved to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem?”This paper provides four systems in Zeeman’s class 30 to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem and gives an answer to the above question.展开更多
基金supported by Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander,Colombia,project 3704.
文摘In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.
文摘本文研究了移动环境下一类具有时滞的Lotka-Volterra合作系统行波解的存在性。利用单调迭代方法,通过构造合适的上下解,证明了当环境运动速度c>max{ c1∗,c2∗}时,系统连接两边界平衡点的行波解的存在性。Existence of traveling wave front solutions is established for diffusive and cooperative Lotka-Volterra system with delays in a shifting environment. Using the method of monotone iteration and by constructing appropriate upper and lower solutions, it is proven that when the environmental movement speed is c>max{ c1∗,c2∗}, there exist traveling wave solutions that connect the boundary equilibrium points of the system.
文摘考虑在移动环境下局部扩散三种群Lotka-Volterra竞争合作系统行波解的存在性,并假设此系统的内禀增长率函数恒大于某正常数。通过构造一对有序的上下解并利用单调迭代技巧和波动引理,证明了系统的非负受迫行波的存在性。We consider the existence of traveling wave solutions for Lotka-Volterra competitive-cooperative system with three-species under a shifting habitat, and assume that the intrinsic growth rate functions of this system are greater than the normal numbers. We prove the existence of non-negative forced traveling waves of the system by constructing a pair of upper and lower solutions and using monotonic iterative techniques and the fluctuation lemma.
文摘为了描述移动环境轻度恶化对两个弱合作物种的持久性产生的影响,本文考虑一类带有与时空均相关的恒正内禀增长函数的格上Lotka-Volterra合作系统。通过构造合适的上下解并结合单调迭代的方法证明了系统存在两组受迫行波解。In order to characterize the effect of mild deterioration of the shifting environment on the two weakly cooperative species persistence, we consider a class of the lattice Lotka-Volterra cooperative systems with a constant positive intrinsic growth function that is spatio-temporally correlated. By constructing suitable upper and slower solutions combined with the method of monotone iteration, we prove that there exist two sets of forced traveling wave solutions for the system.
基金supported by the NSF of China (12271226)the NSF of Gansu Province of China (21JR7RA537)+4 种基金the Fundamental Research Funds for the Central Universities (lzujbky-2022-sp07)supported by the Basic and Applied Basic Research Foundation of Guangdong Province (2023A1515011757)the National Natural Science Foundation of China (12271494)the Fundamental Research Funds for the Central Universities,China University of Geosciences (Wuhan) (G1323523061)supported by the NSF of China (12201434).
文摘This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal(convolution)dispersals:{u_(t)=k*u-u+u(1-u-av),x∈R,t∈R,vt=d(k*v-v)+rv(1-v-bu),c∈R,t∈R.(0.1)Here a≠1,b≠1,d,and r are positive constants.By studying the eigenvalue problem of(0.1)linearized at(ϕc(ξ),0),we construct a pair of super-and sub-solutions for(0.1),and then establish the existence of entire solutions originating from(ϕc(ξ),0)as t→−∞,whereϕc denotes the traveling wave solution of the nonlocal Fisher-KPP equation ut=k*u−u+u(1−u).Moreover,we give a detailed description on the long-time behavior of such entire solutions as t→∞.Compared to the known works on the Lotka-Volterra competition system with classical diffusions,this paper overcomes many difficulties due to the appearance of nonlocal dispersal operators.
基金the National Natural Science Foundation of China(NSFC)under Grant No.12171321.
文摘Gyllenberg and Yan(Discrete Contin Dyn Syst Ser B 11(2):347–352,2009)presented a system in Zeeman’s class 30 of 3-dimensional Lotka-Volterra(3D LV)competitive systems to admit at least two limit cycles,one of which is generated by the Hopf bifurcation and the other is obtained by the Poincaré-Bendixson theorem.Yu et al.(J Math Anal Appl 436:521–555,2016,Sect.3.4)recalculated the first Liapunov coefficient of Gyllenberg and Yan’s system to be positive,rather than negative as in Gyllenberg and Yan(2009),and pointed out that the Poincaré-Bendixson theorem is not applicable for that system.Jiang et al.(J Differ Equ 284:183–218,2021,p.213)proposed an open question:“whether Zeeman’s class 30 can be rigorously proved to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem?”This paper provides four systems in Zeeman’s class 30 to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem and gives an answer to the above question.
