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Xia Liu, Mu Mu, and Qiang Wang

from one steady state to another owing to nonlinear instability, as shown in Mu et al. (2004 , 2017 ) and Kerswell et al. (2014) . The initial perturbation that can most easily trigger the transition is called an optimal triggering perturbation. It is therefore interesting to look for the triggering perturbation associated with an LM occurrence because we can easily forecast an LM occurrence if we observe the signal of such an initial perturbation. Furthermore, if the triggering perturbation is

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