Nonlinear Systems: Lotka-Volterra Model

This lecture covers the study of nonlinear systems, focusing on the Lotka-Volterra model as an example. The model describes the evolution of predator and prey populations over time, with a specific focus on the dynamics observed in nature. Through examples like the interaction between lynx and hares in Canada and sardines and sharks in the Trieste Bay, the lecture illustrates the application of the Lotka-Volterra model in real-world scenarios. The lecture also discusses the mathematical formulation of the model, its assumptions, and the global solution properties. Despite the lack of a general analytical solution, the lecture highlights the existence of a global solution for the Lotka-Volterra system, ensuring non-negativity of populations under certain initial conditions.