Stability and Hopf bifurcation analysis in bidirectional ring network model |
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| Institution: | 1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Automotive Engineering, Hunan University, Changsha City 410082, PR China;2. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China;1. Department of Physics, Duke University, Durham, NC 27708, USA;2. NIC, DESY, Platanenallee 6, D-15738 Zeuthen, Germany;3. Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern, Switzerland |
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| Abstract: | Using the system parameter instead of the delay as the bifurcation parameter, linear stability and Hopf bifurcation analysis including its direction and stability of bidirectional ring network model are investigated in this paper. The main tools to obtain our results are the normal form method and center manifold theory. Numerical simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. |
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