Title: Modelling economic cycle fluctuations with delayed feedback mechanisms: a nonlinear AM-CNN-BiLSTM approach

Authors: Hong Zeng

Addresses: School of Modern Business, Jiaxing Vocational and Technical College, Jiaxing 314036, Zhejiang, China

Abstract: The real economy is subject to nonlinear influences such as consumer behaviour, enterprise investment dynamics, and delays in policy adjustments, all of which contribute to the complexity of economic system dynamics. To address the limitations of existing models, this study proposes a nonlinear framework incorporating delayed feedback mechanisms. Specifically, an AM-CNN-BiLSTM model is introduced, which integrates attention mechanisms, convolutional neural networks (CNNs), and bidirectional long short-term memory (BiLSTM) networks to capture sequential dependencies and enhance predictive accuracy. By simulating time-delay effects, the model effectively characterises the dynamic behaviour of economic systems. Experimental results demonstrate the presence of chaotic motion in the economic cycle system under certain parameter settings, as indicated by a maximum Lyapunov exponent of 0.1938. The proposed model exhibits strong predictive performance, achieving R² = 0.9721, RMSE = 0.0552, and MAPE = 0.0235. These findings contribute to a deeper understanding of how delayed feedback mechanisms influence economic fluctuations and offer valuable insights for economic forecasting and policy formulation.

Keywords: nonlinear modelling; economic cycle fluctuations; delayed feedback mechanism; feature screening.

DOI: 10.1504/IJDSDE.2025.148519

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.3, pp.232 - 249

Received: 27 Mar 2025
Accepted: 19 May 2025
Published online: 10 Sep 2025 *

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