No abstract

Abstract-A new emergence mechanism related to the bounded capacity of human cognition 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, which is called human fuzzy rationality. 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. The human 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. This approach is also extended to take into account the effect of imperfect implementation of the desired control strategy and a non-Newtonian model capturing this effect is developed. In particular, it is demonstrated that complex emergent phenomena can be caused by the fuzzy rationality of human behavior.

Phase transitions in a chain of oscillators with dynamical traps is studied numerically. The notion of dynamical traps mimics the basic features caused by the bounded capacity of human cognition in decision-making. In mathematical terms the dynamical traps form a "low" dimensional region in the phase space of a given system where its dynamics is stagnated. It is demonstrated that in the system under consideration noise gives rise to complex emergent phenomena as its intensity grows.