Relaxation Oscillations and Dynamical Properties in a Time Delay Slow–Fast Predator–Prey Model with a Piecewise Smooth Functional Response

In the past few decades, predator–prey model has played an important role in dynamic behavior of populations. Many scholars have studied stability system. Due to complex influence time delay on systems, time-delay systems garnered wide interest. this paper, a classical piecewise smooth slow–fast is considered. The properties system are analyzed by linearization. existence and uniqueness relaxation oscillation then proven through geometric singular perturbation theory entry–exit function. Finally, stable limit cycle obtained. A numerical simulation verifies our results for shows effectiveness method dealing with delays.