Lotka-Volterra Systems

This lecture discusses the Lotka-Volterra system, showing that it has a global solution satisfying certain conditions. It explores the periodic nature of the solutions, the stationary solutions leading to extinction or stability, and the trajectories in the phase space. The analysis of the Jacobian matrix reveals stable and unstable equilibrium points, highlighting the interdependence of species. By integrating the trajectory equations, the lecture demonstrates the closed level curves in the phase diagram, dependent on a constant K. The lecture concludes by emphasizing the periodic and endless behavior of both populations.