Catálogo de publicaciones - libros

This chapter analyzes the evolution of a state variable in one-dimensional, first-order, discrete dynamical systems. It introduces a method of solution for these systems, and it characterizes the trajectory of the state variable, in relation to its steady-state equilibrium, examining the local and global (asymptotic) stability of this steady-state equilibrium.

This chapter characterizes the evolution of a vector of state variables in multi-dimensional, first-order linear systems. It develops a method of solution for these multi-dimensional systems, and it characterizes the trajectory of the vector of state variables, in relation to the system’s steady-state equilibrium, examining the local and global (asymptotic) stability of this steady-state equilibrium.

This chapter characterizes the trajectory of a vector of state variables in multi-dimensional, first-order, linear dynamical systems. It examines the trajectories of these systems when the matrix of coefficients has real eigenvalues and the vector of state variables converges or diverges in a monotonic or oscillatory fashion towards or away from a steady-state equilibrium that is characterized by either a saddle point or a stable or unstable (improper) node. In addition, it examines the trajectories of these linear dynamical systems when the matrix of coefficients has complex eigenvalues and the system is therefore characterized by a spiral sink, a spiral source, or a periodic orbit.

This chapter characterizes the evolution of a vector of state variables in multi-dimensional, first-order, nonlinear systems of difference equations. It utilizes the analysis of linear, multi-dimensional, first-order systems to characterize the trajectory of nonlinear systems via their linearization in the proximity of a steady-state equilibrium, and the examination of the local and the global properties of these systems, based on the .

This chapter characterizes the evolution of a vector of state variables in higher-order systems as well as non-autonomous systems. It establishes the solution method for these higher-order and non-autonomous systems and, it analyzes the factors that determine the qualitative properties of these discrete dynamical systems in the linear and subsequently the nonlinear case.

This chapter provides a complete characterization of several representative examples of two-dimensional dynamical systems. These examples include a first-order linear system with real eigenvalues, a first-order linear system with complex eigenvalues that exhibits periodic orbit, a first-order linear system with complex eigenvalues that exhibits a spiral sink, a first-order nonlinear system characterized by oscillatory convergence, and a second-order one-dimensional system that is converted into a first-order, two-dimensional system characterized by a continuum of equilibria and oscillatory divergence.