Relaxation oscillations and dynamical properties in two time-delay slow-fast modified Leslie-Gower models (Q2210229)

Summary: In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems.