  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.
