Abstract
In this paper, we analyzed generalized synchronization (GS) from the viewpoint of unstable periodic orbits (UPOs) and Lyapunov vectors (LVs) in Lorenz system driven by a Rössler system. First, we found a new bifurcation route via crisis, a rapid increase in the support of the attractor, from strong GS to weak GS that possesses the power-law parameter sensitivity. We then showed that UPOs with positive conditional Lyapunov exponents (CLEs) are embedded within the attractor after the crisis. We also found the bubbling phenomenon in the response system, where a trajectory intermittently moves away from the synchronization manifold. Furthermore, as a result of the LV analysis, we found that non-hyperbolicity near UPOs with positive CLEs becomes strong in the weak GS regime.
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