Abstract
In this paper, a system of three coupled oscillators with delays is investigated. Some sufficient conditions to guarantee the existence of stability and oscillations for the model are obtained. Simulations are provided to demonstrate the proposed results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wirkus, S., Rand, R.: The dynamics of two coupled van der Pol oscillators with delay coupling. Nonlinear Dynam. 30, 205–221 (2002)
Hirano, H., Rybicki, S.: Existence of limit cycles for coupled van der Pol equations. J. Differ. Equat. 195, 194–209 (2003)
Zhang, J.M., Gu, X.S.: Stability and bifurcation analysis in the delay-coupled van der Pol oscillators. Appl. Math. Model 34, 2291–2299 (2010)
Song, Y.L., Han, M.A., Peng, Y.H.: Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays. Chaos Soliton Fract. 22, 1139–1148 (2004)
Yu, C.B., Wei, J.J., Zou, X.F.: Bifurcation analysis in an age-structured model of a single species living in two identical patches. Appl. Math. Model. 34, 1068–1077 (2010)
Li, X.Z., Wang, J., Ghosh, M.: Stability and bifurcation of an SIVS epidemic model with treatment and age of vaccination. Appl. Math. Model. 34, 437–450 (2010)
Rompala, K., Rand, R., Howland, H.: Dynamics of three coupled van der Pol oscillators with application to circadian rhythms. Commun. Nonlinear Sci. Numer. Simul. 12, 794–803 (2007)
Nagy, B.: Comparison of the bifurcation curves of a two-variable and a three-variable circadian rhythm model. Appl. Math. Model. 32, 1587–1598 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lin, Y., Feng, C. (2011). Stability and Oscillation Analysis in a System of Three Coupled Oscillators with Delays. In: Zhou, Q. (eds) Theoretical and Mathematical Foundations of Computer Science. ICTMF 2011. Communications in Computer and Information Science, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24999-0_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-24999-0_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24998-3
Online ISBN: 978-3-642-24999-0
eBook Packages: Computer ScienceComputer Science (R0)