Research for Coupled van der Pol Systems with Parametric Excitation and Its Application
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and
Abstract
In this article, we study the primary resonances of van der Pol systems with parametric excitation using the multiple scales method (MSM) and the homotopy analysis method (HAM). First, we study the nonlinear dynamic response of a coupled system with parametric excitation when the ratio of internal resonances are different, and obtain the four-dimensional average equation of the rectangular coordinate form using the MSM, thereby periodic motions are found in the system. Second, using the HAM, we obtain the four periodic solutions, in which there are two sets of in-phase periodic solutions and two sets of out-of-phase periodic solutions. Finally, we obtain the frequency response curves using the MSM and the HAM, in which it is found that the differences could be ignored.
Acknowledgements
The authors gratefully acknowledge the support of the National Natural Science Foundations of China (NNSFC) through grant no. 11572288. We are also grateful to the anonymous reviewers for their constructive comments and suggestions.
Competing interests: The authors declare that there are no conflict of interests regarding the publication of this article.
Authors’ contributions: All the authors contributed equally and significantly in writing this article. All the authors read and approved the final manuscript.
Appendix
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©2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
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- The DFT Calculations of Structures and EPR Parameters for the Dinuclear Paddle-Wheel Copper(II) Complex {Cu2(μ2-O2CCH3)4}(OCNH2CH3) as Powder or Single Crystal
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- Research for Coupled van der Pol Systems with Parametric Excitation and Its Application
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Articles in the same Issue
- Frontmatter
- Ultrasonic Investigations on Polonides of Ba, Ca, and Pb
- The DFT Calculations of Structures and EPR Parameters for the Dinuclear Paddle-Wheel Copper(II) Complex {Cu2(μ2-O2CCH3)4}(OCNH2CH3) as Powder or Single Crystal
- Characteristics of Polarisation in the Ramsauer–Townsend Minima in Strongly Coupled Semiclassic Plasmas
- Streaming Jeans-Alfvén Instability in Quantum Magnetoplasmas
- Research for Coupled van der Pol Systems with Parametric Excitation and Its Application
- Interaction of Three Interfacial Cracks between an Orthotropic Half-Plane Bonded to a Dissimilar Orthotropic Layer with Punch
- Conservation Laws and Nonlocally Related Systems of Two-Dimensional Boundary Layer Models
- Localised Nonlinear Waves in the Three-Component Coupled Hirota Equations
- Nonlinear Stage of Modulation Instability for a Fifth-Order Nonlinear Schrödinger Equation
