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On the new results of global attractive set and positive invariant set of the Lorenz chaotic system and the applications to chaos control and synchronization

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science in china(series F) 2005年第3期48卷 304-321页

作者： liao xiaoxin 1, 2, 3 , FU Yuli 4.& XIE shengli 4.1. Department of Control science & Control engineering, Huazhong university of science & {4., Wuhan 4.0074. china 2. school of Automation, Wuhan university of science & {4., Wuhan 4.0070, china 3. school of information, Central south university of Economy, Politics and Law, Wuhan 4.0064. china 4. school of electronics & information engineering, south china university of technology, guangzhou 51064., china Correspo{24.ce should be addressed to liao xiaoxin (email: xiaoxin_liao@***) 1. Department of Control science & Control engineering Huazhong University of Science & Technology 430074 Wuhan China 2. school of Automation Wuhan University of Science & Technology 430070 Wuhan China 3. school of information Central South University of Economy Politics and Law 430064 Wuhan China 4. school of elect{3.cs & information {4. South China University of Technology 510640 Guangzhou China

Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov. Our uniform formula can derive a series of the new estimations. Employing the idea of intersection in set theory, we extract a new Leonov formula-like estimation from the family of the estimations. With our method and the new estimation, one can confirm that there are no equilibrium, periodic solutions, almost periodic motions, wandering motions or other chaotic attractors outside the global attractive set. The Lorenz butterfly-like singular attractors are located in the global attractive set only. This result is applied to the chaos control and chaos synchronization. some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution, or globally stabilize an unstable (or locally stable but not globally asymptotically stable) equilibrium. Further, some new global exponential chaos synchronization results are presented. Our new method and the new results are expected to be applied in real secure communication systems.

关键词： Lorenz chaotic system global attractive set positive invariant set globally exponential tracking globally exponential synchronization.

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Recent Progress in Atmospheric Chemistry Research in china: Establishing a Theoretical Framework for the “Air Pollution Complex”

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Advances in Atmospheric sciences 2023年第8期40卷 1339-1361页

作者： Tong ZHU Mingjin TANG Meng GAO Xinhui BI Junji CAO Huizheng CHE Jianmin CHEN Aijun DING Pingqing FU Jian GAO Yang GAO Maofa GE Xinlei GE Zhiwei HAN Hong HE Ru-Jin HUANG Xin HUANG Hong liao Cheng LIU Huan LIU Jianguo LIU shaw Chen LIU Keding LU Qingxin MA Wei NIE Min sHAO Yu sONG Yele sUN Xiao TANG Tao WANG Tijian WANG Weigang WANG Xuemei WANG Zifa WANG Yan YIN Qiang ZHANG Weijun ZHANG Yanlin ZHANG Yunhong ZHANG Yu ZHAO Mei ZHENG Bin ZHU Jiang ZHU Peking university Beijing 100871China guangzhou Institute of Geochemistry Chinese Academy of SciencesGuangzhou 510640China Hong Kong Baptist university Hong Kong SARChina Institute of Atmospheric Physics Chinese Academy of SciencesBeijing 100029China Chinese Academy of Meteorological sciences Beijing 100081China Fudan university Shanghai 200438China Nanjing university Nanjing 210023China Tianjin university Tianjin 300072China Chinese Research Academy of Environmental sciences Beijing 100012China Ocean university of china Qingdao 266100China Institute of Chemistry Chinese Academy of SciencesBeijing 100190China Nanjing university of information science and technology Nanjing 210044China Research Center for Eco-Environmental sciences Chinese Academy of SciencesBeijing 100085China Institute of Earth Environment Chinese Academy of SciencesXi’an 710061China university of science and technology of china Hefei 230026China Tsinghua university Beijing 100084China Anhui Institute of Optics and Fine Mechanics Hefei Institutes of Physical ScienceChinese Academy of SciencesHefei 230031China Jinan university Guangzhou 510632China Hong Kong Polytechnic university Hong Kong SARChina Beijing Institute of technology Beijing 100081China

Atmospheric chemistry research has been growing rapidly in china in the last 25 years since the concept of the“air pollution complex”was first proposed by Professor Xiaoyan TANG in *** papers published in 2021 on air pollution(only papers included in the Web of science Core Collection database were considered),more than 24.00 papers were authored or co-authored by scientists working in *** this paper,we review a limited number of representative and significant studies on atmospheric chemistry in china in the last few years,including studies on(1)sources and emission inventories,(2)atmospheric chemical processes,(3.interactions of air pollution with meteorology,weather and climate,(4.interactions between the biosphere and atmosphere,and(5)data *** intention was not to provide a complete review of all progress made in the last few years,but rather to serve as a starting point for learning more about atmospheric chemistry research in *** advances reviewed in this paper have enabled a theoretical framework for the air pollution complex to be established,provided robust scientific support to highly successful air pollution control policies in china,and created great opportunities in education,training,and career development for many graduate students and young *** paper further highlights that developing and low-income countries that are heavily affected by air pollution can benefit from these research advances,whilst at the same time acknowledging that many challenges and opportunities still remain in atmospheric chemistry research in china,to hopefully be {4. over the next few decades.

关键词： atmospheric chemistry air pollution complex theoretical framework recent progress

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