2011/01/17 by Suman Acharyya, R. E. Amritkar · 1 citation
Physics and Astronomy · #nlin.CD
paper · pdf · doi:10.1063/1.3581154
published as Chaos 21, 023113 (2011) · 11 pages, 6 figures
arxiv created 2011/01/17 · arxiv updated 2015/03/17
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 and in the desynchronized state one is positive while the other is negative implying that one oscillator is trying to fly away while the other is holding it. We give a simple model of coupled integrable systems that shows a similar phenomena and can be treated as the normal form for the desynchronization bifurcation. We conclude that the desynchronization is a pitchfork bifurcation of the transverse manifold.