Bifurcations of limit cycles in a quintic Lyapunov system with eleven parameters |
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| Authors: | Li Feng |
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| Affiliation: | 1. College of Materials Science and Engineering, China Jiliang University, Hangzhou 310018, PR China;2. College of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, PR China;1. Department of Chemical Engineering, Institute of Chemical Technology, Matunga, Mumbai 400019, India;2. Chemical Engineering Division, Bhabha Atomic Research Center, Trombay, Mumbai 400085, India;3. Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India;1. School of Mining, College of Engineering, University of Tehran, Tehran 1439957131, Iran;2. Sarcheshmeh Copper Complex, Research and Development Centre, Rafsanjan 7731643181, Iran |
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| Abstract: | In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 12 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 12 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems, the result of Jiang et al. (2009) [18] was improved. |
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