Title: Slow-Fast Dynamics and Its Application to an Ecological Model

Abstract:  Slow-fast dynamics refers to a class of mathematical models that arise in systems with widely differing timescales. In many real-world scenarios, such as in biology, ecology, chemistry, and physics, different processes occur at different timescales. Understanding how these fast and slow processes interact can lead to profound insights into the overall behavior of the system. In this talk, I will introduce the concept of multi-timescale models (also referred to as slow-fast models) and the existence of intricate patterns such as relaxation oscillations and canard cycles within slow-fast dynamical models. These phenomena help us understand the behavior of complex systems.In the second part of the talk, I will discuss the practical application of slow-fast dynamics in population dynamics. Focusing on a predator-prey model with a Holling-type functional response, we identify and analyze the rich and complex dynamics within the ecological system. Through this analysis, we can understand the complex ecological interactions, offering valuable insights into the delicate balance of predator and prey.