Transitions between Metastable Long-Run Consumption Behaviors in a Stochastic Peer-Driven Consumer Network

Abstract

We study behavioral change - as a transition between coexisting attractors - in the context of a stochastic, non-linear consumption model with interdependent agents. Relying on the indirect approach to the analysis of a stochastic dynamic system, and employing a mix of analytical, numerical and graphical techniques, we identify conditions under which such transitions are likely to occur. The stochastic analysis depends crucially on the stochastic sensitivity function technique as it can be applied to the stochastic analoga of closed invariant curves [14], [1]. We find that in a moderate noise environment increased peer influence actually reduces the complexity of observable long-run consumer behavior. © 2021 American Institute of Mathematical Sciences. All rights reserved.Acknowledgments. Tatyana Perevalova and Jochen Jungeilges gratefully acknowledge research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2021-1387)