Interaction between economies in a business cycle model

• Published in: Chaos, solitons and fractals solitons and fractals, 2022-02, Vol.155, p.111672, Article 111672
• Main Authors: Amaral, Amaury S., Camargo, Victor E., Crepaldi, Antônio F., Ferreira, Fernando F.
• Format: Article
• Language: English
• Subjects: Macrodynamics; Multistability; Stability analysis; Synchronization
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2021.111672

•The proposed model emulates a macroeconomic system to study economic cycles.•We find multistability where chaotic attractors coexist with limit cycle attractors.•By using the master stability function method we establish the intervals of the control parameter in which the system synchronizes in a stable way. In this work we study the interaction between two or three nonlinear dynamical macroeconomic idealized systems. The model is a modified version of the Bouali’s system. Only three economic variables were considered: foreign capital inflow, household savings, and the gross domestic product. It was studied possible patterns that can result from these dynamics as well as structural changes when the coupling parameter (inflow of external capital) varies, here chosen as control parameter. Firstly, the present model has multistability where limit cycles and strange attractors depend on the initial conditions. Moreover, to some values of the control parameter occurs synchronization between the economies. However, there is a range of control parameters where they can be unstable. So, we applied the Master Stability Function method in order to evaluate the stability analysis. We found the occurrence of stable synchronization when the coupling of the economies is symmetrical (bidirectional interaction) or asymmetrical (unidirectional). Instability is predominant for higher control parameter values.