Transitions and chaos of a business cycle model

Litian Huang; Huichao Wang; Litian Huang; Huichao Wang

doi:10.3934/era.2026081

Electronic Research Archive

2026, Volume 34, Issue 3: 1809-1831. doi: 10.3934/era.2026081

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Research article

Transitions and chaos of a business cycle model

Litian Huang ¹,
Huichao Wang ^{2
,
,}

1.
School of Business, Chengdu College of University of Electronic Science And Technology of China, Sichuan 610054, China
2.
School of Science, Xuchang University, Henan 461000, China

Received: 17 December 2025 Revised: 07 February 2026 Accepted: 10 February 2026 Published: 27 February 2026

This study investigates a modified Bouali model (referred to as the business cycle model) through the lens of transition dynamics theory. Under reasonable theoretical assumptions, we identify the output-capital ratio $ c $ as the key parameter that determines the transition and chaos in the business cycle model. Through rigorous mathematical analysis, we demonstrate that this model exhibits both jump (discontinuous) and continuous transitions as the output-capital ratio $ c $ increases and crosses a critical value. In particular, for the output-capital ratio large enough $ c $, the business cycle model develops a strange attractor, which means that there exists chaos in this business cycle model.
- dynamic transition,
- chaos,
- business cycle model,
- bifurcation
Citation: Litian Huang, Huichao Wang. Transitions and chaos of a business cycle model[J]. Electronic Research Archive, 2026, 34(3): 1809-1831. doi: 10.3934/era.2026081

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Abstract

This study investigates a modified Bouali model (referred to as the business cycle model) through the lens of transition dynamics theory. Under reasonable theoretical assumptions, we identify the output-capital ratio $ c $ as the key parameter that determines the transition and chaos in the business cycle model. Through rigorous mathematical analysis, we demonstrate that this model exhibits both jump (discontinuous) and continuous transitions as the output-capital ratio $ c $ increases and crosses a critical value. In particular, for the output-capital ratio large enough $ c $, the business cycle model develops a strange attractor, which means that there exists chaos in this business cycle model.

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