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.

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.

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.

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.

Competitive analysis of price online inventory problem with cost function

In this paper,a new price is given to the online decision maker at the beginning of each day.The trader must decide how many items to purchase according to the current price.We present three variants and an online algorithm based on cost function.The competitive ratio of the online algorithm is given for each variant,which is a performance measure of an online algorithm.More importantly,we show that the online algorithm is optimal.

Disparities in tree mortality among plant functional types(PFTs)in a temperate forest:Insights into size-dependent and PFT-specific patterns

Tree mortality significantly influences forest structure and function,yet our understanding of its dynamic patterns among a range of tree sizes and among different plant functional types(PFTs)remains incomplete.This study analysed size-dependent tree mortality in a temperate forest,encompassing 46 tree species and 32,565 individuals across different PFTs(i.e.,evergreen conifer vs.deciduous broadleaf species,shade-tolerant vs.shade-intolerant species).By employing all-subset regression procedures and logistic generalized linear mixed-effects models,we identified distinct mortality patterns influenced by biotic and abiotic factors.Our results showed a stable mortality patte rn in eve rgreen conifer species,contrasted by a declining pattern in deciduous broadleaf and shadetolerant,as well as shade-intolerant species,across size classes.The contribution to tree mortality of evergreen conifer species shifted from abiotic to biotic factors with increasing size,while the mortality of deciduous broadleaf species was mainly influenced by biotic factors,such as initial diameter at breast height(DBH)and conspecific negative density.For shade-tolerant species,the mortality of small individuals was mainly determined by initial DBH and conspecific negative density dependence,whereas the mortality of large individuals was subjected to the combined effect of biotic(competition from neighbours)and abiotic factors(i.e.,convexity and pH).As for shade-intolerant species,competition from neighbours was found to be the main driver of tree mortality throughout their growth stages.Thus,these insights enhance our understanding of forest dynamics by revealing the size-dependent and PFT-specific tree mortality patterns,which may inform strategies for maintaining forest diversity and resilience in temperate forest ecosystems.

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.

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].

Uniform persistence of multispecies ecological competition predator-pray system with Holling Ⅲ type functional response

The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species and among prey species are simultaneously considered. By using the comparison theory and qualitative analysis, the sufficient conditions for uniform strong persistence are obtained.

Existence of Competitive Equilibria without Standard Boundary Behavior

We study the existence of competitive equilibria when the excess demand function fails to satisfy the standard boundary behavior. We introduce alternative boundary conditions and we examine their role in proving the existence of strictly positive solutions to a system of non-linear equations (competitive equilibium prices). In addition, we slightly generalize a well-known theorem on the existence of maximal elements, and we unveil the link between the hypothesis of our theorem and one of the boundary conditions introduced in this work.

The permanence and global attractivity of a competitive system with feedback controls and toxic substance

In this paper,we consider a nonautonomous competitive system with feedback controls and toxic substance.Some average couditions for the permanence and global attractivity of the system are obtained.It is shown that our results are generalization or improvement of those of Zhao,Jiang and Lazer [Nonlinear Analysis:Real World Applications,5(4)(2004),265-276],Xia,Cao,Zhang and Chen [Journal of Mathematical Analysis and Applications,294(2)(2004),503-522] and Chen [Nonlinear Analysis:Real World Applications,in press]

Dynamics of a Two Species Competitive System with Pure Delays

A class of non-autonomous two species Lotka-Volterra competitive system with pure discrete time delays is discussed. Some sufficient conditions on the boundedness, permanence, periodic solution and global attractivity of the system are established by means of the comparison method and Liapunov functional.

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.

适应不确定性:菲律宾对冲战略的演变逻辑

2010年以来,菲律宾的对冲战略经历了短暂调整、瓦解、重塑与再次调整4个阶段。如何解释菲律宾对冲战略的演变动态?在美国强化对华竞争的背景下,第三方国家对冲实施的历时性变化成为日益重要的研究议题。对冲战略的实施演变理论上可分为维持、调整与瓦解三种状态。应对不确定性是对冲实施的基本逻辑,其在不确定性条件下具有明显的功能。在中美菲三方关系结构下,菲律宾领导人需要不断评估外部威胁与安全承诺两类具体的不确定性因素,对两类不确定性的评估影响了对冲战略的功能,进而引发其实施演变。阿基诺三世政府对冲战略的短暂调整与瓦解、杜特尔特政府对冲战略的重塑与维持,以及杜特尔特执政后期尤其是小马科斯执政后对冲战略再次转向选边立场的调整,是领导人为实现利益最大化、不断评估和适应不确定性的结果。该研究有助于进一步理解不确定性与对冲实施的关系,对于分析对冲实施的动态变化问题具有现实意义。

中国国家治理结构下“地方法治竞争”范式的反思

法治是现代治理的基本方式,法治建构受制于国家治理结构。“地方法治竞争”范式能否成立,需纳入整体性的国家治理制度逻辑与观念传统之中进行考察。通过“地方法治竞争”推动法治国家建构,实际面临诸多现实制约和实践难题,受限于观念上的工具主义法治观、体制结构中的一统格局和国家权力的功能主义,这三者具有深层的历史文化与社会结构根源。因此,探索法治国家建构的中国道路,需深入国家治理观念与政治社会结构,更新对法治理念及其构成元素的理解,走出工具主义法治观,在中国国家治理架构下自上而下推动,逐步走向“治理主义”法治观,认知法治的治理功能,并且将“法律正义”视为一种公共产品。

在线平台竞争功能组合对创作者内容采纳的影响研究——来自视频弹幕类平台的实证检验

[目的/意义]为在线平台创作者生成内容优化,以及在线平台内容采纳率提升提供新思路。[研究设计/方法]将传统应用于企业竞争策略组合研究的竞争组合理论,拓展到在线平台个人信息情境。以视频弹幕类在线平台“哔哩哔哩”为例,基于二手数据抓取,分析在线平台竞争功能组合的数量、复杂度与异质性对创作者内容采纳的影响。[结论/发现]在线平台情境下,竞争功能组合的数量与异质性会显著正向影响创作者的内容采纳,而竞争功能组合的复杂度会显著负向影响创作者的内容采纳。同时,竞争功能组合数量、复杂度与异质性的影响作用存在交互性。[创新/价值]为视频弹幕类平台的内容生态优化以及创作者的内容采纳率提升提供借鉴,丰富用户行为与信息服务研究的理论和实践体系。

基于功能诉求的攀岩运动员个性化体能训练方案设计

文章运用文献资料法和逻辑分析法,厘清体能训练功能与运动员特定诉求契合理念,探讨攀岩运动员个性化体能训练功能效果与自身特定训练诉求之间的对应关系。运动员体能训练表现出平衡、专门、进阶与叠加四大特定诉求,体能训练基于契合运动员诉求,展示出针对性、精确性和功能性的功能效果。攀岩运动员个性化体能训练方案,基于应答攀岩运动员特定的平衡、专门、进阶与叠加诉求,体现出功能变化的基本设计思路。文章列举不同竞技水平、不同攀岩专项的三名运动员,进行基于功能诉求的个性化体能训练方案设计,为其个性化的体能训练设计和应用实践,提供部分内容借鉴的思路参考。

体育智能裁判系统对竞技体育的赋能、挑战与应对

作为人工智能与体育裁判结合的体育智能裁判系统对竞技体育产生了极大影响,有必要对其进行系统的评估和研究。运用文献分析法、规范分析法等研究方法分析了体育智能裁判系统对竞技体育的影响,旨在更好地实现体育智能裁判系统对竞技体育的助力。研究表明,体育智能裁判系统通过发挥辅助功能、替代功能和学习功能增强了体育裁判的精准性和公平性,提升了竞技者的竞技水平,促进了竞技体育的发展,但其又存在着技术、价值和法律风险,给竞技体育带来了挑战。对此,应当通过功能论正确认识体育智能裁判系统的功能定位,以技术手段和规则体系弥补和消除其对竞技体育的反功能,更好地发挥体育智能裁判系统对竞技体育的作用。

暌违与聚合:“功能性-传统”训练的理性审视与超越路径

为有针对性地提升运动员竞技能力、规避伤病以应对竞技体育职业化挑战,功能性训练被引入运动训练领域,丰富了竞技运动训练体系,但也由此导致新的理论与实践问题。对功能性训练的概念、内容进行系统梳理与审视发现:功能性训练的内涵与外延分别存在龃龉,体现为核心内涵的淡化、外延的泛化及不当分隔;引入功能性训练后出现理论困境与挑战,体现为功能性训练与传统训练概念对应失准、与经典运动训练理论架构悬殊且存在逻辑交叠以及理论发展中的概念嬗变、实践转向与价值泛化。以上问题表明,当前“功能性-传统”训练概念、理论和应用步入误区,应超越简单的“二元对立”,形成训练理论间多维聚合的发展路径。提出:顺应功能性训练与传统训练的共同理念,构建“协同互补”的运动训练理论体系;综合两者方法体系,设计“多点发力”的内容与方法库;监控训练风险,形成“互联兼合”的负荷管理与功能筛查系统。

N-种群Lotka-Volterra扩散竞争反馈控制生态系统的持久性和全局渐近性

本文研究了一类具有αi类功能性反应函数的n种群非自治Lotka-Volterra扩散竞争反馈控制生态系统的持久性和全局渐近性.利用比较原理和构造Lyapunov函数分别得到系统的持久生存与全局渐近稳定的充分条件.