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.

AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

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.

Discussion on the Application of Technical and Tactical Skills in Mixed Martial Arts Competitions

This article mainly analyzes the application of technical and tactical skills in mixed martial arts competitions,including mixed martial arts and its competition characteristics,the main application significance of technical and tactical skills in mixed martial arts competitions,and its primary application strategies.It is hoped that this analysis can provide some guidelines for the appropriate application of mixed martial arts athletes’technical and tactical skills to improve their winning rate in mixed martial arts competitions.

Research on the Role of Guiding Students to Participate in Skills Competitions on the Development of Young Teachers in Vocational Colleges

This paper explores the role of guiding students to participate in skills competitions on the development of young teachers in vocational colleges.We investigate the impact of skills competitions on the consolidation of professional knowledge,development of innovation capabilities,improvement of hands-on abilities,and enhancement of communication skills with students.The results of this research demonstrate that skills competitions have a positive influence on the professional growth of young teachers.The consolidation of professional knowledge,development of innovation capabilities,improvement of hands-on abilities,and enhancement of communication skills collectively contribute to the effectiveness of young teachers in vocational colleges.It is recommended that vocational colleges prioritize and support the participation of young teachers in skills competitions to foster their professional development.

Teaching Design and Implementation of the Electrical and Electronic Technology Course Based on Teaching Ability Competition

The teaching ability competition is a vital method for stimulating teachers’enthusiasm and enhancing their teaching skills.This approach has gained increasing attention from colleges and universities in recent years.The competition focuses on evaluating teachers’capabilities in designing and implementing lessons,encouraging the exchange of new educational ideas and high-quality teaching methods.Reforming the teaching of Electrical and Electronic Technology courses based on insights from teaching competitions can significantly improve teaching quality.This paper explores the teaching design and implementation of the Electrical and Electronic Technology course,drawing on the principles of teaching ability competitions.First,it analyzes the existing problems in teaching this course.Then,it highlights the significant benefits that teaching competitions bring to the course.Based on these insights,the paper proposes practical strategies aimed at enhancing students’interest and practical skills,thereby promoting innovative developments in teaching Electrical and Electronic Technology.

Global stability of bistable traveling wavefronts for a three-species Lotka-Volterra competition system with nonlocal dispersal

This paper is devoted to the study of traveling wavefronts for a three-component Lotka-Volterra system with nonlocal dispersal.This system arises in the study of three-species competition model in which there is no competition between two of these three species.It has been shown that this system admits a bistable traveling wavefront.In this paper,we further investigate the stability of bistable traveling wavefronts.By constructing suitable super-and sub-solutions and using a dynamical system approach,we obtain the globally asymptotic stability of the bistable traveling wavefronts.

The Model of“Post,Course,Competition,Certificate”Integrated Education for Electronic Information Engineering Technology Major in Higher Vocational Colleges

The core education function of higher vocational colleges is to train technical talents with high quality,so as to meet the needs of talents in the development stage of our society.Under the guidance of talent training,higher vocational colleges need to pay attention to establishing an all-round and three-dimensional education model,and promote innovation of higher vocational education on the basis of this.It is also a way to promote the innovation of higher vocational education to vigorously promote the construction of“post,course,competition,certificate”mode in the construction of education mode.Through the construction of“post,course,competition,certificate”mode,the education mode of higher vocational colleges is gradually improved,so as to strengthen the effectiveness of talent training in higher vocational colleges.Therefore,in this paper,the author puts forward some suggestions to promote the construction of the integrated education mode of the electronic information engineering technology major in higher vocational colleges,so as to help improve the talent training level of higher vocational colleges.

Periodicity and Stability in Periodic n-Species Lotka-Volterra Competition System with Feedback Controls and Deviating Arguments

By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.

Developing nonlinear additive tree crown width models based on decomposed competition index and tree variables

Crown development is closely related to the biomass and growth rate of the tree and its width(CW)is an important covariable in growth and yield models and in forest management.To date,various CW models have been proposed.However,limited studies have explicitly focused on additive and inherent correlation of crown components and total CW as well as the influence of competition on crown radius from the corresponding direction.In this study,two model systems were used,i.e.,aggregation method system(AMS)and disaggregation method system(DMS),to develop crown width additive model systems.For calculating spatially explicit competition index(CI),four neighbor tree selection methods were evaluated.CI was decomposed into four cardinal directions and added into the model systems.Results show that the power model form was more proper for our data to fit CW growth.For each crown radius and total CW,height to the diameter at breast height(HDR)and basal area of trees larger than the subject tree(BAL)significantly contributed to the increase of prediction accuracy.The 3-m fixed radius was optimal among the four neighborhoods selection ways.After adding decomposed competition Hegyi index into model systems AMS and DMS,the prediction accuracy improved.Of the model systems evaluated,AMS based on decomposed CI provided the best performance as well as the inherent correlation and additivity properties.Our study highlighted the importance of decomposed CI in tree CW modelling for additive model systems.This study focused on methodology and could be applied to other species or stands.

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.

Competitive oxidation behavior of Ni-based superalloy GH4738 at extreme temperature

A high thrust-to-weight ratio poses challenges to the high-temperature performance of Ni-based superalloys. The oxidation behavior of GH4738 at extreme temperatures has been investigated by isothermal and non-isothermal experiments. As a result of the competitive diffusion of alloying elements, the oxide scale included an outermost porous oxide layer (OOL), an inner relatively dense oxide layer (IOL), and an internal oxide zone (IOZ), depending on the temperature and time. A high temperature led to the formation of large voids at the IOL/IOZ interface. At 1200℃, the continuity of the Cr-rich oxide layer in the IOL was destroyed, and thus, spallation occurred. Extension of oxidation time contributed to the size of Al-rich oxide particles with the increase in the IOZ. Based on this finding,the oxidation kinetics of GH4738 was discussed, and the corresponding oxidation behavior at 900-1100℃ was predicted.

GPU parallel computation of dendrite growth competition in forced convection using the multi-phase-field-lattice Boltzmann model

A graphics-processing-unit(GPU)-parallel-based computational scheme is developed to realize the competitive growth process of converging bi-crystal in two-dimensional states in the presence of forced convection conditions by coupling a multi-phase field model and a lattice Boltzmann model.The elimination mechanism in the evolution process is analyzed for the three conformational schemes constituting converging bi-crystals under pure diffusion and forced convection conditions,respectively,expanding the research of the competitive growth of columnar dendrites under melt convection conditions.The results show that the elimination mechanism for the competitive growth of converging bi-crystals of all three configurations under pure diffusion conditions follows the conventional Walton-Chalmers model.When there is forced convection with lateral flow in the liquid phase,the anomalous elimination phenomenon of unfavorable dendrites eliminating favorable dendrites occurs in the grain boundaries.In particular,the anomalous elimination phenomenon is relatively strong in conformation 1 and conformation 2 when the orientation angle of unfavorable dendrites is small,and relatively weak in conformation 3.Moreover,the presence of convection increases the tip growth rate of both favorable and unfavorable dendrites in the grain boundary.In addition,the parallelization of the multi-phase-field-lattice Boltzmann model is achieved by designing the parallel computation of the model on the GPU platform concerning the computerunified-device-architecture parallel technique,and the results show that the parallel computation of this model based on the GPU has absolute advantages,and the parallel acceleration is more obvious as the computation area increases.

具有时滞和线性收获项的三维Lotka-Volterra合作系统的Hopf分支

针对三维Lotka-Volterra合作系统的Hopf分支进行了研究。首先,在三维Lotka-Volterra合作系统的基础上,引入时滞项及线性收获项对该系统进行改进;其次,以时滞τ作为分支参数,对改进后系统的局部Hopf分支的存在性进行分析,给出使系统在正平衡点处产生Hopf分支的临界值;然后,利用中心流形定理和规范型理论计算出Hopf分支方向及周期解稳定性的公式;最后,进行数值模拟,根据数值模拟的结果,验证了理论的可行性。结果表明,当时滞τ从0一直增加到超过临界值时,系统的正平衡点由稳定状态变为不稳定状态,且在正平衡点处产生Hopf分支。说明时滞影响了系统的动力学行为,使其动力学性质更加复杂。

基于Lotka-Volterra种群动态模型的水生动物性别比例变化研究

水生动物的性别比例会受遗传因素与外界环境、激素的影响,其具有适应性别比例变异的特征,且性别比例变化对种群自身及其他物种都有一定影响。主要从物种间的内部机制与外部资源环境因素两方面论述。通过已知性别决定因素,构造性别比例变化与资源可用性相关函数,考虑性别比例变化与生存环境面积的影响,建立基于Lotka-Volterra的系统动态模型。本文以海七鳃鳗为例,运用模型进行研究,研究得到其在性别比例变化下种群数量变化曲线随时间呈周期性,且猎食者的数量波动相比于猎物的数量呈现约四分之一个周期的滞后效应。

Competitive effect, but not competitive response, varies along a climatic gradient depending on tree species identity

Background: Understanding the role of species identity in interactions among individuals is crucial for assessing the productivity and stability of mixed forests over time. However, there is limited knowledge concerning the variation in competitive effect and response of different species along climatic gradients. In this study, we investigated the importance of climate, tree size, and competition on the growth of three tree species: spruce(Picea abies), fir(Abies alba), and beech(Fagus sylvatica), and examined their competitive response and effect along a climatic gradient.Methods: We selected 39 plots distributed across the European mountains with records of the position and growth of 5,759 individuals. For each target species, models relating tree growth to tree size, climate and competition were proposed. Competition was modelled using a neighbourhood competition index that considered the effects of inter-and intraspecific competition on target trees. Competitive responses and effects were related to climate.Likelihood methods and information theory were used to select the best model.Results: Our findings revealed that competition had a greater impact on target species growth than tree size or climate. Climate did influence the competitive effects of neighbouring species, but it did not affect the target species? response to competition. The strength of competitive effects varied along the gradient, contingent on the identity of the interacting species. When the target species exhibited an intermediate competitive effect relative to neighbouring species, both higher inter-than intraspecific competitive effects and competition reduction occurred along the gradient. Notably, species competitive effects were most pronounced when the target species' growth was at its peak and weakest when growing conditions were far from their maximum.Conclusions: Climate modulates the effects of competition from neighbouring trees on the target tree and not the susceptibility of the target tree to competition. The modelling approach should be useful in future research to expand our knowledge of how competition modulates forest communities across environmental gradients.

Research on the Reform of the Course“Reading of Concrete Structure Plan and Construction Drawings”Under the Background of“Promoting Teaching and Learning Through Competitions”

The inherent teaching approach can no longer meet the demands of society.In this paper,current issues within the teaching landscape of architectural engineering technology in higher vocational colleges as well as the policies and teaching demands that formed the basis of this model were analyzed.The study shows the importance of the implementation of the teaching model“promoting teaching and learning through competitions.”This model puts emphasis on the curriculum and teaching resources,while also integrating the teaching process and evaluation with competition.These efforts aim to drive education reform in order to better align with the objectives of vocational education personnel training,while also acting as a reference for similar courses.

Empowering Vocational Students to Excel in Skills Competitions:Challenges and Recommendations

This paper analyzes the key challenges faced by vocational college students when participating in national skills competitions.It identifies problems such as limited resources,insufficient training,lack of mentorship,academic workload constraints,and inadequate equipment.Targeted solutions are proposed,including improving resource access,providing structured skill training,implementing expert mentorship programs,offering flexible schedules,and upgrading experimental equipment.Implementing these recommendations through a collaborative effort among stakeholders can significantly empower vocational students to excel in skills competitions by enabling access to resources,building practical skills,obtaining guidance,managing time effectively,and gaining hands-on experience.

Research on the Cultivation Path of Craftsmanship Spirit in Vocational Colleges: from the Perspective of Skills Competition

The spirit of craftsmanship is gaining increasing attention from both society and the education community.Along with professional knowledge,continuous research,and innovation have become decisive factors in determining the quality of products.In this context,vocational colleges strive to cultivate high-quality skilled talents,making the cultivation of craftsmanship spirit a crucial component of vocational education.This study explores the cultivation path of craftsmanship spirit through the lens of skills competitions,with a special emphasis on developing students’perseverance.The research conclusions of this article hold significant reference value for the implementation of vocational education policies.

Enhancing Vocational Education through Innovative Skills Competitions: Challenges and Solutions

This study investigates the challenges encountered by vocational colleges when preparing for innovative skills competitions and proposes effective countermeasures.It highlights issues concerning students’motivation,limited financial resources and hardware,teacher capacity limitations,inadequate reward systems,and curriculum misalignment.Through meticulous research and analysis,this paper presents practical recommendations to mitigate these challenges.Suggestions encompass strategies to enhance students’motivation,increase financial support,provide professional development opportunities for teachers,revamp the reward system,and align the curriculum with competition requirements.By implementing these measures,vocational colleges can cultivate active student participation,elevate teaching quality,bridge the gap between education and industry demands,and equip students for success in innovative skills competitions.

一类分数阶Lotka-Volterra系统的动力学研究

本文建立了一个新的分数阶Lotka-Volterra模型.首先,我们考虑所涉及的分数阶Lotka-Volterra模型的存在性、唯一性和非负性.其次,通过分析特征方程将时滞视为分岔参数,建立一个新的充分条件来保证系统的稳定性和Hopf分岔的出现.