Modeling the Chaos and Bifurcation in Solow’s Business Trade Cycle Model by Using Delay Differential Equations

This research extends the traditional Solow model by introducing a delay parameter via a delay differential equation to examine the dynamics of business cycles. Alongside the Solow farmwork, the Harrod-Domar model and a modified Solow model are considered to provide a broader perspective on growth dynamics and stability analysis. This study reveals that the inclusion of delays causes fluctuations in stability, leading to Hopf bifurcation, limit cycles, and chaotic behavior, thereby capturing the complex evolution of the trade cycle. The dynamics highlight how minor changes in the system parameters can reshape long-term economic trajectories. The analysis, conducted using MATLAB, underscores the significance of the Solow and Harrod-Domar models, as well as their variants, for understanding economic growth and industrial development. This approach helps stakeholders predict and mitigate economic changes by identifying key thresholds and dynamic patterns, thereby promoting resilience, stability, and long-term growth.