Libro

Descripción

The theory of dynamical systems is a comprehensive framework used to solve nonlinear systems of differential equations, with a focus on studying the changes in processes over time. The field of nonlinear dynamics has many implications in mathematical sciences, particularly in the study of complex dynamical systems related to biological population models.
In this book, we propose and analyze several discrete-time population models, examining their qualitative behavior with regards to stability of equilibria, bifurcation analysis, and chaos control. The first model we discuss is a prey-predator interaction model related to a discrete-time plant-herbivore system that includes a weak predator functional response. We formulate this model to study the interaction between grape vines and apple twig borers. We also analyze the local dynamics of fixed points, as well as the transcritical bifurcation, Neimark-Sacker bifurcation, and chaos control of this system.