Desynchronization bifurcation of coupled nonlinear dynamical systems

We analyze the desynchronization bifurcation in the coupled Rössler oscillators. After the bifurcation the coupled oscillators move away from each other with a square root dependence on the parameter. We define system transverse Lyapunov exponents (STLE), and in the desynchronized state one is posit...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2011-06, Vol.21 (2), p.023113-023113-7
Main Authors: Acharyya, Suman, Amritkar, R. E.
Format: Article
Language:English
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Summary:We analyze the desynchronization bifurcation in the coupled Rössler oscillators. After the bifurcation the coupled oscillators move away from each other with a square root dependence on the parameter. We define system transverse Lyapunov exponents (STLE), and in the desynchronized state one is positive while the other is negative. We give a simple model of coupled integrable systems with quadratic nonlinearity that shows a similar phenomenon. We conclude that desynchronization is a pitchfork bifurcation of the transverse manifold. Cubic nonlinearity also shows the bifurcation, but in this case the STLEs are both negative.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.3581154