Introduzione all'analisi qualitativa dei sistemi dinamici discreti e continui

[Autom. eng. transl.] The text was conceived for the structure of the current degree courses in Biology, Mathematics, Applied Mathematics, Engineering, Natural and Medical Sciences. It focuses on the qualitative aspects of differential equations such as limitations or limitlessness of solutions, existence or non-existence of periodic orbits, stability or instability of equilibrium points, bifurcation of the system when a parameter varies, robustness of the system in the presence of perturbations. The qualitative analysis of discrete and continuous dynamical systems is a technically accessible topic also for first-level students and allows us to connect, combine and exercise concepts coming from algebra, basic differential calculus and elementary geometry, stimulating intuition mathematics. The volume is characterized by two aspects: the inductive and the figurative. The inductive approach is based on a wide range of problems solved and designed to gradually introduce both theoretical knowledge and qualitative analysis techniques. The figurative aspect is expressed through more than 350 images that show the trends of the solutions or phase portraits and which summarize the information obtained through the qualitative analysis. In Part I we deal with nonlinear discrete models, both in real and in complex fields, while Part II is devoted to continuous models, differential equations and systems of two nonlinear equations.