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Quantum bifurcation has been studied with two approaches: indirect and direct. Indirect Quantum Bifurcation to be observed requires a quantum system and its analogical classical system where the quantum behavior is observed at the critical parameter setting determined at the moment when bifurcation occurs in the classical system. Direct Quantum Bifurcation, as proposed by [Yang and Weng 2010], is a method to study quantum bifurcation behavior in its original sense, as the change of characteristics of quantum trajectories and fixed points of nonlinear quantum dynamics.
 Yanan Liu, Sen Kuang, Shuang Cong, “Lyapunov-Based Feedback Preparation of GHZ Entanglement of N-Qubit Systems”, IEEE transactions on cybernetics, 2016