一类交替变化的竞争—合作混杂种群模型研究  

Study on a Class of Alternative Competition-Cooperation Hybrid Population Model

作　　者：苗新艳[1,2] 张龙 罗颜涛[2] 潘丽君 MIAO Xinyan;ZHANG Long;LUO Yantao;PAN Lijun(College of Mathematics and Physics,Xinjiang Agricultural University,Urumqi Xinjiang 830052,China;College of Mathematics and System Science,Xinjiang University,Urumqi Xinjiang 830046,China;College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing Jiangsu 211106,China)

机构地区：[1]新疆农业大学数理学院,新疆乌鲁木齐830052 [2]新疆大学数学与系统科学学院,新疆乌鲁木齐830046 [3]南京航空航天大学理学院,江苏南京211106

出　　处：《广西师范大学学报（自然科学版）》2018年第3期25-31,共7页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11361059;11271312);新疆维吾尔自治区自然科学基金(2014721014);江苏省自然科学基金青年基金(BK20130779)

摘　　要：经典的Lotka-Volterra种间模型研究只关注单纯的种间竞争关系或者单纯的种间合作关系。然而由于现实环境的复杂性及生物种群间关系的多样性,种群间的相互关系往往不是单一的而是多种关系的混合体。本文建立一类两种群Lotka-Volterra竞争—合作混杂系统,竞争关系及合作关系共同出现在2个种群之间,受环境影响在不同时间区间交替变化。通过构造适当的Lyapunov函数及分析等手段,得到关于系统正性、有界性及正平衡点的全局渐近稳定性等问题的充分性判定准则,并给出数值模拟验证所得结论。研究发现,竞争—合作混杂模型相较于单一的竞争模型或合作模型有更丰富的动力学行为,生物种群展现更多可实现的生存性,与现实环境更加接近。The classical Lotka-Volterra model study focuses only on simple interspecific competition or simple interspecific cooperation.Due to the complexity of the real environment and the diversity of the relationship between biological populations,the interrelationship between populations is often not a single one but a mixture of multiple relationships.In this paper,a class of two-species Lotka-Volterra competition-cooperation hybrid system is established.The competitive relationship and cooperative relationship occur among the two populations,which are alternately affected by environmental impact in different time intervals.By constructing appropriate Lyapunov functions and analysis,sufficient criterion is obtained for the global asymptotic stability of the system’s positivity,bounded and positive equilibrium point,then data is given for simulation to verify the conclusion.Through the study,it is found that the competition-cooperation model has more dynamic behavior than the single competition model or cooperative model,and the biological population shows more survivability,which is more consistent with the real environment.

关 键 词：竞争-合作混杂系统 种群 正性 有界性 全局渐近稳定性 

分 类 号：O175[理学—数学]