Stochastic stability and bifurcation in a macroeconomic model |
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| Affiliation: | 1. School of Science, Hunan City University, Yiyang 413000, P. R. China;2. Department of Mechanical Engineering, University of Manitoba, Winnipeg, R3T 5V6, Canada;3. Department of Mathematics, The University of Poonch Rawalakot, Azad Kashmir 10250, Pakistan;4. European University Institute, Department of Economics, Via delle Fontanelle, 18, I-50014, Florence, Italy;5. Rimini Centre for Economic Analysis (RCEA), LH3079, Wilfrid Laurier University, 75 University Ave W., ON, N2L3C5, Waterloo, Canada;6. Research Group in Electronic, Biomedical and Telecommunication Engineering, University of Castilla-La Mancha (UCLM), 16071, Cuenca, Spain;7. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia;8. Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia;9. Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China;10. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China |
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| Abstract: | On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis. |
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