Abstract
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.
Original language | English |
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Article number | 023113 |
Journal | Chaos |
Volume | 21 |
Issue number | 2 |
DOIs | |
State | Published - 1 Apr 2011 |
Externally published | Yes |