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Stability and Oscillatory Behavior of the Solutions on a Class of Coupled Van der Pol-Duffing Equations with Delays
Mathematics and Computer Science
Volume 4, Issue 6, November 2019, Pages: 104-111
Received: Oct. 31, 2019; Accepted: Nov. 29, 2019; Published: Dec. 10, 2019
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Chunhua Feng, Department of Mathematics and Computer Science, Faculty of Alabama State University, Montgomery, USA
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In the present paper, a class of coupled van der Pol-Duffing oscillators with a nonlinear friction of higher polynomial order model which involves time delays is investigated. The coefficients of the highest order of the polynomial determine the boundedness of the solutions. With special attention to the boundedness of the solutions and the instability of the unique equilibrium point of linearized system, some sufficient conditions to guarantee the existence of oscillatory solutions for the model are obtained based on the generalized Chafee's criterion. Convergence of the trivial solution is determined by the negative real part of eigenvalues of the linearized system. Examples are provided to demonstrate the reduced conservativeness for the parameters of the proposed results. The results obtained shown that the passive decay rate in the model affects the oscillatory frequency and amplitude. When a permanent oscillation occurred, time delays affect mainly oscillatory frequency and amplitude slightly.
Coupled Van der Pol-Duffing Equation, Delay, Stability, Oscillation
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Chunhua Feng, Stability and Oscillatory Behavior of the Solutions on a Class of Coupled Van der Pol-Duffing Equations with Delays, Mathematics and Computer Science. Vol. 4, No. 6, 2019, pp. 104-111. doi: 10.11648/j.mcs.20190406.12
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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