Desynchronization bifurcation of coupled nonlinear dynamical systems |
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Authors: | Acharyya Suman Amritkar R E |
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Institution: | Theoretical Physics Division, Physical Research Laboratory, Navrangpura, Ahmedabad, Gujarat 380009, India. suman@prl.res.in |
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Abstract: | We analyze the desynchronization bifurcation in the coupled Ro?ssler 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. |
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