ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL

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.

Positive Solutions Bifurcating from Zero Solution in a Lotka-Volterra Competitive System with Cross-Diffusion Effects

A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.

EXISTENCE OF POSITIVE SOLUTION FOR A TWO-PATCHES COMPETITION SYSTEM WITH DIFFUSION AND TIME DELAY AND FUNCTIONAL RESPONSE

By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].

Deviations of Steady States of the Traveling Wave to a Competition Diffusion System with Random Perturbation

This paper considers the asymptotic dynamics of steady states to the Lotka-Volterra competition diffusion systems with random perturbations by two-parameter white noise on the whole real line. By the fundamental solution of heat equation, we get the asymptotic fluctuating behaviors near the stable states respectively. That is, near the steady state (u,v)=(0,1), the mean value Eu(x,t) is shifted above the equilibrium u=0 and Ev(x,t) is shifted below the equilibrium v=1. However, near the steady state (u,v)=(1,0), the mean value Eu(x,t) is shifted below the equilibrium u =1 and Eu(x,t)=0.

Spatial Segregation Limit of a Quasilinear Competition-Diffusion System

The aim of this paper is to investigate a Volterra-Lotka competition model of quasilinear parabolic equations with large interaction. Some existence, uniqueness and convergence results for the system are given. Also investigated is its spatial segregation limit when the interspecific competition rates become large. We show that the limit problem is similar to a free boundary problem.

Existence of Two Limit Cycles in Zeeman’s Class 30 for 3D Lotka-Volterra Competitive System

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.

PERSISTENCE OF TWO-SPECIES AYALA COMPETITIVE MODEL WITH DIFFERENT DIFFUSIONS

In this paper, the stabilities of boundary equilibrium and positive equilibrium of two_species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At the same time, the dynamic behaviors between systems with diffusion and those without diffusion are compared. This shows the influence of diffusions on the persistence of species.

A Class of Singularly Perturbed Problems for Nonlinear Two-Species Competitive Reaction-Diffusion System

A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.

NONTRIVIAL SOLUTIONS OF COMPETITIVE-DIFFUSIVE SYSTEMS WITH SMALL DIFFUSION

We discuss nontrivial steady-state solutions of a competitive-diffusive systems with small diffusion in which two interacting species u and v inhibit the same bounded region. By using methods of bifurcation theory and indefinite weight function, we prove the existence and uniqueness of solutions which are positive in both u and v and asymptotically stable corresponding to the case where the populations can co-exist.

GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS

A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.

Diffusion and Adsorption of Tetralin Hydrocracking Reaction on Different Zeolites by Molecular Simulation

Three different zeolite catalysts with different pore sizes(MFI-type,BEA-type,and FAU-type zeolites)have been prepared.The influence of different zeolite catalysts on reactivity and product shape selectivity of tetralin is investigated.Clear differences are observed in the reactivity of tetralin and distribution of products achieved by different catalysts.The diffusion and adsorption behavior of the reactant tetralin and its intermediates,n-butylbenzene and 1-methylindane under the reaction conditions are simulated using molecular simulation methods.Upon combining simulation results and experimental observations,it is shown that the difference in diffusion coefficient and competitive adsorption capacity can explain the reactivity of tetralin and the selectivity of products.The steric hindrance of the MFI-type zeolite mainly limits the key step of ring opening of tetralin,leading to lower selectivity of ring-opening products.n-Butylbenzene molecules can diffuse sufficiently fast in the large pores of FAU-type zeolite and the weak adsorption capacity of n-butylbenzene leads to its insufficient cracking.In addition,it also explains the reason that the BEA-type zeolite has the best BTX selectivity,because it can satisfy both good ring-opening activity and sufficient butylbenzene cracking depth.

Interspecific Competition Between Levanderina fissa(Dinophyceae) and the Other Three Microalgal Species in Co-Cultures

Growth interactions between the dinoflagellate Levanderina fissa (=Gyrodinium instriatum) and the other three algal bloom species Skeletonema costatum (Bacillariophyceae), Prorocentrum micans (Dinophyceae), and Chattonella marina (Raphido- phyceae) were studied using bi- or tri-algal co-cultures under laboratory conditions. The Lotka-Volterra model was applied to esti- mate the interspecific competition between them. Results showed that the growth of L. fissa was significantly suppressed in both bi-algal and tri-algal cultures, and the maximum cell densities in co-cultures were only between 21% and 69% of that in mono-cul- ture. L. fissa outcompeted P. micans;however, its effects on S. costatum and C. marina were generally less than the effects of their intraspecific competitions based on the competition coefficients. Contrarily, the inhibitory effects of S. costatum and C. marina on L. fissa were much greater. S. costatum outcompeted the other three species in all co-cultures, and its competition coefficients on the other species were more than 10000 times higher than the opposite. The growth of C. marina was suppressed by S. costatum;how- ever, it outcompeted L. fissa and P. micans. The growth of P. micans was most strongly inhibited in co-cultures, and the maximum cell densities in co-cultures were less than 15% of that in mono-species culture. The results suggested that L. fissa had few advan- tages in the interspecific competition. The adaptation to low salinity and the utilization of organic phosphorus might be the important reasons for L. fissa to take the competitive predominance in brackish estuarine environments.

GLOBAL ATTRACTIVITY IN A N-SPECIES COMPETITION DIFFERENCE SYSTEM

A population of interacting species is considered which is governed by a system of nonlinear difference equation.In the case of the interacting species with competition,a sufficient condition for global attractivity of an equilibrium state is derived.The result can be considered as a best discrete approximation of the continuous system.

Partial extinction, permanence and global attractivity innonautonomous n-species Lotka-Volterra competitivesystems with impulses

In this paper, the qualitative properties of general nonautonomous Lotka-Volterran-species competitive systems with impulsive e？ects are studied. Some new criteria on thepermanence, extinction and global attractivity of partial species are established by used themethods of inequalities estimate and Liapunov functions. As applications, nonautonomous twospecies Lotka-Volterra systems with impulses are discussed.

Effect of inorganic salts on Se(Ⅳ) and Re(Ⅶ) diffusions in bentonite

Diffusion behaviors of Se(IV) and Re(VII) in bentonite were investigated by a through-diffusion method in nitrate, sulfate, carbonate and silicate solutions. SEM-EDS analysis showed that Se(IV) was reduced to red precipitate Se(0) by sulfite. Se(IV) was sorbed on bentonite with distribution coefficient Kd of(2.6–5.3)×10-4m3/kg in sulfite, nitrate and sulfate solutions, whereas it was hardly sorbed in carbonate and silicate solutions. The effective diffusion coefficients were De =(0.81–7.0)×10-11m2/s for Se(IV) and De =(1.4–4.4)×10-11m2/s for Re(VII). The De value of Se(IV) exhibited a dependence on the inorganic salts in the order of sulfite ≈ nitrate ≈ sulfate > silicate > carbonate, whereas the salts had insignificant effect on Re(VII) diffusion. The results suggest that the discrepancy in diffusion mechanism may lead to the different impact of the salts on the diffusion of Se(IV) and Re(VII) in GMZ bentonite.

具有非线性交叉扩散的Lotka-Volterra竞争系统的共存解

考虑一类齐次Dirichlet边界条件下具有非线性交叉扩散的Lotka-Volterra竞争系统的共存解问题.首先,借助线性算子的谱理论分析该问题平凡解和半平凡解的稳定性;其次,利用正锥上的不动点指数理论给出该问题共存解存在的充分条件.

带自扩散和交错扩散的三种群Lotka-Volterra竞争模型解的一致有界性和稳定性

应用能量估计方法和Gagliardo-Nirenberg型不等式,讨论了带自扩散和交错扩散的三种群Lotka-Volterra竞争模型解的一致有界性和整体存在性,并由Lyapunov函数证明了该模型正平衡点的全局渐近稳定性．

石英纳米孔中氦气与甲烷竞争扩散的分子模拟

氦气具有尺寸小、扩散和渗透能力强等特点,其独特的物理性质严重制约了氦气的聚集成藏。因此,深入揭示地质条件下氦气与甲烷的竞争扩散规律,是系统认识富氦天然气成藏机制的重要途径。首次采用分子模拟技术,构建了石英纳米狭缝-通道孔复合模型,探索了甲烷与氦气的混合气体在模型中的竞争扩散规律。分子模拟结果表明,甲烷对氦气的扩散有抑制作用,并且甲烷对吸附态氦气有较强的驱替能力;当氦气在混合气体中摩尔分数达90%时,游离态的氦分子可聚合形成直径更大的氦团簇,氦团簇的出现对氦气存储以及储氦库建设具有一定的启示。此外,当扩散通道孔的直径小于甲烷和氦气的动力学直径2倍时,甲烷和氦气无法从石英纳米通道扩散出去,此时分子间的排斥力很强,将阻止气体分子的进一步逸散,有利于氦气保存。研究结果提供了在原子分子水平下氦气与甲烷在石英纳米孔中的竞争逸散规律,为氦气的富集和保存机制研究提供了有用信息,并为氦气资源的勘探与开发提供了参考依据。

城市数字技术创新产出的空间策略互动行为研究

区域数字创新协同发展是实现我国国家治理能力与治理体系现代化的重要驱动力。现有文献主要关注区域间数字技术创新产出的空间相关性和异质性,未对其是否存在空间策略互动行为及其作用机制进行识别和检验。本文将技术创新扩散和创新竞争规避效应假说引入城市数字技术创新产出空间特征分析中,通过构建空间计量模型分析城市数字技术创新产出的空间策略互动行为。研究结果表明:第一,本地数字技术创新产出数量的上升会带动空间关联地区数字技术创新产出数量的上升,并且在数字经济发展水平空间权重矩阵下,数字技术创新产出的空间溢出效应高于技术进步空间权重矩阵下的空间溢出效应。从策略互动形式来看,城市间数字技术创新产出表现出明显的向上竞争效应。第二,机制检验表明,城市间数字技术创新产出空间互动效应是由省界竞争规避机制驱动的,城市内部学习示范效应会弱化城市间数字技术创新产出的空间策略互动效应,外部学习示范机制会强化城市间数字技术创新产出的空间策略互动效应。第三,异质性检验表明,数字技术创新产出表现出明显的技术进步、数字经济发展水平异质性;高(低)数字技术创新产出城市间存在显著空间策略互动效应。研究结论对正确认识城市间数字技术创新产出的空间策略互动行为和建立健全区域间数字技术进步协同促进机制具有重要的现实意义。

基于Lotka-Volterra的创新产品扩散仿真研究

针对市场竞争背景下创新产品扩散问题的特殊性,本文首先运用消费者行为理论,从体验论视角逻辑推演消费者行为的动态历程。然后借鉴Bass与Lotka-Volterra模型对竞争环境下消费者感知行为进行了具体描述与数理建模,在此基础上,利用交互建模技术对创新产品扩散过程建模仿真。最后,通过两种情景数值分析比较与实例分析验证模型的有效性。研究表明:企业的竞争能力越强,创新产品的市场占有额越高,且对消费者感知价值呈现正向影响,消费者感知价值可以促进消费者的二次购买行为;正面口碑与广告正向影响消费者的购买决策;负面口碑负向影响消费者的购买决策。