This book is the second volume in a two-part series on the theory of ordinary differential equations and their applications to population dynamics.  While the first volume provides an introduction to the topic, this second volume presents advanced mathematical tools for analyzing such problems.  Part I focuses on refined techniques for describing the long-term behavior of these systems. It includes a detailed discussion of dissipative dynamical systems, omega and alpha limit sets, global attractors, bifurcations, the construction of smooth center manifolds, and normal form theory.  Part II introduces new perspectives on predator-prey systems by applying theoretical results to derive oscillating solutions through Hopf bifurcation, traveling invasion waves using global attractor theory, and a description of long-term dynamics in competitive interactions between predator variants.  Throughout the book, concepts are illustrated with numerical examples, and MATLAB codes are provided.  Bridging an interdisciplinary gap, this book will be valuable to graduate students and researchers studying mathematical models in population dynamics.