An explicit recursive formula for computing the normal forms associated with semisimple cases |
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| Affiliation: | 1. Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210023, PR China;2. School of Automation, Southeast University, Nanjing, 210096, PR China;3. Institute of Information and Control Engineering Technology, Nanjing Normal University, Nanjing, Jiangsu 210042, PR China;4. College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing, Jiangsu 210042, PR China;1. College of Science, Shandong University of Science and Technology, Qingdao 266590, PR China;2. Shandong Key Laboratory of Robotics and Intelligent Technology, Qingdao 266590, PR China;1. School of Mathematical Sciences and Physics, North China Electric Power University, Beijing 102206, China;2. School of Economics and Management, North China Electric Power University, Beijing 102206, China;1. MOE Key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;2. College of Information Engineering, Tarim University, Alar, Xinjiang 843300, China;3. School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, China;1. Université d’Avignon et des Pays de Vaucluse, UMR 1114 EMMAH, F-84018 Avignon Cedex, France;2. UMR 1114 EMMAH, Centre INRA d’Avignon, F-84914 Avignon Cedex 9, France;1. Grupo de Neurocomputación Biológica, Dpto. de Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, Spain;2. Instituto de Seguridad de la Información, Consejo Superior de Investigaciones Científicas, Serrano 144, 28006 Madrid, Spain |
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| Abstract: | This paper presents an explicit, computationally efficient, recursive formula for computing the normal forms, center manifolds and nonlinear transformations for general n-dimensional systems, associated with semisimple singularities. Based on the formula, we develop a Maple program, which is very convenient for an end-user who only needs to prepare an input file and then execute the program to “automatically” generate the result. Several examples are presented to demonstrate the computational efficiency of the algorithm. |
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| Keywords: | Differential system Semisimple singularity Normal form Center manifold Computational efficiency Maple |
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