While human control behavior is well-understood in continuous control tasks, little is known about how human operators detect sudden changes in the controlled element dynamics. This paper focuses on modeling this detection phase for pursuit tracking tasks. Potential triggers for the human operator to detect changes in the controlled element dynamics were investigated via a time-varying computer simulation. Based on the results, hypotheses were generated and later tested in a single-axis pursuit tracking experiment with fifteen participants, where good-quality data were collected. Transitions from approximate single to approximate double integrator dynamics and vice versa were investigated, and participants indicated if they detected the transition by pressing a button. Using the button push data, a model for each transition was developed and validated. The models work under the assumption that human operators use a threshold, a multiple of the steady-state standard deviation, on certain signals to detect transitions. The models developed for the transition from single to double integrator dynamics and vice versa are based on the tracking error and system output acceleration, respectively. They have an accuracy of 88.9\% and 99.4\%, respectively. However, the estimation of the detection lags remains a limitation of both models. Nonetheless, this research helped confirm the tracking error can be used in a model for the transition from single to double integrator dynamics, proposed a model for the opposite transition, and identified that the relationship between control inputs and the system's response is an important factor in the detection phase.