Mathematical modeling of trend cycle: Fad, fashion and classic - Bae, Hyeong Ohk; Cho, Seung Yeon; Yoo, Jane; Yun, Seok Bae (Physica D: Nonlinear Phenomena, 2025)
In this work, we suggest a system of differential equations that 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.
Keywords: Classic; Condition; Expressive power; Fad; Fashion; Mathematical modeling; SIR type model; System of differential equations; Trend cycle; Underlying dynamics; Classic; Fad; Fashion; Mathematical modeling; SIR type model; Trend cycle