Codimension-2 bifurcations of the Kaldor model of business cycle |
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| Authors: | Xiaoqin P Wu |
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| Institution: | 1. School of Mathematical and Natural Sciences, Arizona State University, 4701 W. Thunderbird Rd, Glendale, AZ 85306, USA;2. Department of Mathematics, SUNY - New Paltz, 1 Hawk Drive, New Paltz, NY 12561, USA;1. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;2. Research Center for Complex models and Network Sciences, and Department of Mathematics, Southeast University, Nanjing 210096, China |
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| Abstract: | In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov–Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results. |
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