Chaotic dynamics in an overlapping generations model: Forecasting and regularization

Abstract

Irregular dynamics (especially chaotic) is often undesirable in economics because it presents challenges for predicting and controlling the behavior of economic agents. In this paper, we used an overlapping generations (OLG) model with a control function in the form of government spending as an example, to demonstrate an effective approach to forecasting and regulating chaotic dynamics based on a combination of classical control methods and artificial intelligence algorithms. We showed that in the absence of control variables, both regular and irregular (including chaotic) behavior could be observed in the model. In the case of irregular dynamics, a small control action introduced in the model allows modifying the behavior of economic agents and switching their dynamics from irregular to regular mode. We used control synthesis by the Pyragas method to solve the problem of regularizing the irregular behavior and stabilizing unstable periodic orbits (UPOs) embedded in the chaotic attractor of the model. To maximize the basin of attraction of stabilized UPOs, we used several types of evolutionary algorithms (EAs). We compared the results obtained by applying these EAs in numerical experiments and verified the outcomes by numerical simulation. The proposed approach allows us to improve the forecasting of dynamics in the OLG model and make agents’ expectations more predictable.