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.
Bae was supported by the Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education and Technology (NRF-2021R1A2C1093383). Cho was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2022-00166144). Yoo was supported by Ajou University Research Fund, Ministry of Education, Science and Technology and National Research Fund of Korea (NRF-2022S1A5C2A02090368). Yun was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2023R1A2C100573712).
