LI Jun, CHEN Yu-shu. Transition Sets of Bifurcations of Dynamical System With Two State Variables With Constraints[J]. Applied Mathematics and Mechanics, 2012, 33(2): 135-152. doi: 10.3879/j.issn.1000-0887.2012.02.001
 Citation: LI Jun, CHEN Yu-shu. Transition Sets of Bifurcations of Dynamical System With Two State Variables With Constraints[J]. Applied Mathematics and Mechanics, 2012, 33(2): 135-152.

# Transition Sets of Bifurcations of Dynamical System With Two State Variables With Constraints

##### doi: 10.3879/j.issn.1000-0887.2012.02.001
• Received Date: 2011-08-19
• Rev Recd Date: 2011-12-04
• Publish Date: 2012-02-15
• Bifurcation of periodic solutions widely exists in nonlinear dynamical systems. Categories of bifurcations of systems with two state variables with different types of constraints were discussed where some new types of transition sets were added. Additionally, the bifurcation properties of two-dimensional systems without constraints were compared with the ones with constraints. The results obtained can be used by engineers for the choice of the structural parameters of the system.
•  [1] Chen Y S, Langford W F. The subharmonic bifurcation solution of nonlinear Mathieu’s equation and Euler dynamically buckling problems[J]. Acta Mechanica Sinica, 1988, 20(6): 522-632. [2] 陈予恕, 丁千. C-L方法及其在工程非线性动力学问题中的应用[J]. 应用数学和力学, 2001, 22(2): 127-134.(CHEN Yu-shu, DING Qian. C-L method and its application to engineering nonlinear dynamical problems[J]. Applied Mathematics and Mechanics(English Edition), 2001, 22(2): 144-153.) [3] Chen Y S, Xu J. Universal classification of bifurcating solutions to a primary parametric resonance in van der Pol-Duffing-Mathicu’s systems[J].J Science in China, 1996, 39(4): 405-417. [4] 吴志强, 陈予恕. 具有单边约束的基本分岔问题的新分岔模式[J]. 应用数学和力学, 2001, 22(11): 1135-1141.(WU Zhi-qing, CHEN Yu-shu. New bifurcation patterns in elementary bifurcation problems with single-side constraint[J]. Applied Mathematics and Mechanics(English Edition), 2001, 22(11): 1260-1267.) [5] 吴志强, 陈予恕. 含约束非线性动力系统的分岔分类[J]. 应用数学和力学, 2002, 23(5): 477-482.(WU Zhi-qing, CHEN Yu-shu. Classification of bifurcations for nonlinear dynamical problems with constraints[J]. Applied Mathematics and Mechanics(English Edition), 2002, 23(5): 535-541.) [6] Wu Z Q, Yu P, Wang K Q. Bifurcation analysis on a self-excited hysteretic system[J]. International Journal of Bifurcation and Chaos, 2004, 14(8): 2825-2842. [7] 吴志强, 丁然, 陈予恕. 约束含参分岔问题的分类[J]. 应用数学和力学, 2010, 31(2): 127-133.(WU Zhi-qing, DING Ran, CHEN Yu-shu. Classification of parametrically constrained bifurcations[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(2): 135-142.) [8] 胡凡努, 李养成. 关于两个状态变量组的等变分歧问题的通用开折[J]. 数学理论与应用, 2000, 20(3): 50-57.(HU Fan-nu, LI Yang-cheng. Versal unfolding of equivariant bifurcation problems with two types of state variables[J]. Mathematical Theory and Application, 2000, 20(3): 50-57.（in Chinese）) [9] 秦朝红, 陈予恕, 李军. 1∶1内振悬索的二维奇异性分析[J]. 应用数学和力学, 2010, 31(2): 134-142.(QIN Zhao-hong, CHEN Yu-shu, LI Jun. singularity analysis of a two-dimensional elastic cable with 1∶1 internal resonance[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(2): 143-150.) [10] Golubitsky M, Schaeffer D G. Singularities and Groups in Bifurcation Theory[M]. NY: Spring-Verlag, 1985. [11] Chen Y S, Qin Z H. Singular analysis of two-dimensional bifurcation system[J].Science China Technological Sciences, 2010, 53(3): 608-611.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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