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李先义,原扬州大学、深圳大学、南华大学数学教授,博导,现为浙江科技学院教授,博导,非线性分析研究所所长;浙江省“钱江学者”特聘教授;华东师范大学本、硕、博,法国里尔科技大学博士后。主要研究方向:常微分方程与动力系统,生物数学,数学建模与仿真;主要研究兴趣:稳定性理论,分支与混沌理论。至今已在欧美等著名期刊发表科研论文90余篇,其中SCI收录50篇(按2018年JCR分区一区、二区共40篇),EI收录31篇,CPCI-S收录2篇,Top期刊4篇;被SCI它引200余次,单篇它引最高92次;完整解决了JDEA等上面提出的多个“Open Problems and Conjectures”;在德国出版专著一部。主持科研项目20余项(国家级4项),参加完成国家级2项、省部级3项;先后被评为“湖南省青年骨干教师”、“湖南省新世纪‘121’人才工程”人选、“湖南省学科带头人”、 “广东省‘千百十’人才工程省级培养对象”等;获“湖南省高校科技工作先进工作者”、“上海市研究生优秀成果”(优博)、全国第三届“秦元勋常微分方程奖”等科研奖励与荣誉10多项。任多个国际期刊的主编、副主编、荣誉编委、编委,美国“数学评论”特约评论员,Nonl.Dyn.,IJBC, JMAA, CMA,Nonl. Dyn.等40余种期刊的审稿专家,中国博士后科学基金、国家自然科学基金(面上、地区、青年)、省自然科学基金(一般、青年、杰青、重点)、科技进步奖、博士毕业论文盲审等方面的评审专家。
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报告内容简介
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After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0.
All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means — both “locally” and “globally” and both “finitely” and “infinitely” — to comprehensively explore a given system.
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