Dynamical Traps Caused by Fuzzy Rationality as a New Emergence Mechanism

TL;DR

This paper introduces a new emergence mechanism caused by fuzzy rationality, where individuals' inability to distinguish similar strategies creates dynamical traps that induce instability and complex behavior in systems.

Contribution

It proposes a novel emergence mechanism based on fuzzy rationality leading to dynamical traps, and analyzes their effects on system stability through numerical simulations.

Findings

Dynamical traps create regions where control is suspended.

These traps induce instability and complex dynamics.

Numerical analysis of oscillator chains demonstrates these effects.

Abstract

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.