A new emergence mechanism related to the human fuzzy rationality is considered. It assumes that individuals (operators) governing the dynamics of a certain system try to follow an optimal strategy in controlling its motion but fail to do this perfectly because similar strategies are indistinguishable for them. The main attention is focused on the systems where the optimal dynamics implies the stability of a certain equilibrium point in the corresponding phase space. In such systems the fuzzy rationality gives rise to some neighborhood of the equilibrium point, the region of dynamical traps, wherein each point is regarded as an equilibrium one by the operators. So when the system enters this region and while it is located in it, maybe for a long time, the operator control is suspended. To elucidate a question as to whether the dynamical traps on their own can cause emergent phenomena the stochastic factors are eliminated from consideration. In this case the system can leave the dynamical trap region only because of the mismatch between actions of different operators. By way of example, a chain of oscillators with dynamical traps is analyzed numerically. As demonstrated the dynamical traps do induce instability and complex behavior of such systems.
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