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A simple algorithm for testing the stability of periodic solutions of some nonlinear oscillators with large time delay |
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| Authors: | LI JunYu ZHANG Li & WANG ZaiHua State Key Laboratory of Mechanics Control of Mechanical Structures Nanjing University of Aeronautics Astronautics Nanjing China |
| Affiliation: | LI JunYu 1,2,ZHANG Li 1 & WANG ZaiHua 1,3 1 State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China,2 Institute of Mathematics,Physics and Information Science,Zhejiang Ocean University,Zhoushan,316000,China 3 Institute of Science,PLA University of Science and Technology,Nanjing 211101 |
| Abstract: | Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W function, this paper presents a simple algorithm for locating the rightmost characteristic root of periodic solutions of some nonlinear oscillators with large time delay. As application, the proposed algorithm is used to study the primary resonance and 1/3 subharmonic resonance of the Duffing ... |
| Keywords: | time-delay system weakly nonlinear stability periodic solution characteristic function Lambert W function |
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