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We present a linearly stable model in two complex dimensions that can be triggered by an initial perturbation or external noise to exhibit chaotic dynamics although all linear perturbations are damped. The transition to chaos is caused by an interplay between transient linear growth and nonlinear, energy conserving mixing. The linear growth mechanism is due to the non-normality of the linearized dynamics in the vicinity of the stationary point. We consider this combined mechanism of non-normal growth and nonlinear mixing as a model for a new but often realized transition scenario from laminar flow to turbulence.
Gebhardt et al. (Tue,) studied this question.