2023/04/20 by Hyeong‐Ohk Bae, Bae, Hyeong-Ohk, Seung Yun Cho +5 · 1 citation
Decision Sciences · Physics and Astronomy · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Complex Network Analysis Techniques #FOS: Mathematics #Innovation Diffusion and Forecasting #Opinion Dynamics and Social Influence
paper · pdf · doi:10.48550/arxiv.2304.10225
openalex publication_date 2023/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we suggest a system of differential equations that quantitatively models the formulation and evolution of a trend cycle through the consideration of underlying dynamics between the trend participants. Our model captures the five stages of a trend cycle, namely, the onset, rise, peak, decline, and obsolescence. It also provides a unified mathematical criterion/condition to characterize the fad, fashion and classic. We prove that the solution of our model can capture various trend cycles. Numerical simulations are provided to show the expressive power of our model.