Using MatContM in the study of a nonlinear map in economics

MatContM is a MATLAB interactive toolbox for the numerical study of iterated smooth maps, their Lyapunov exponents, fixed points, and periodic, honioclinic and heteroclinic orbits as well as their stable and unstable invariant iwniifolds. The bifurcation;1.t aysis is based on continuation methods, tracing out solution iiianifolds of various types of objects while some of the parameters of the map vary. In particular, MatContM computes codimension 1 bifurcation curves of cycles and supports the computation of the normal form coefficients of their codimension two bifurcations, and allows branch switching from codimension 2 points to secondary curves. MatContM builds on an earlier command-line MATLAB package Cl_MatContM but provides new coinputational routines and functionalities, as well as a graphical user interface, enabling internctive, control of all computations, data handling and archi Ong. We, apply MatContM in our study of the monopoly model of T. Puu with cubic price and quadratic marginal cost functions. Using MatContM, we analyze the fixed points and their stability and we compute branches of solutions of period 5, 10, 13 17. The chaotic and periodic behavior of the monopoly model is further analyzed by computing the largest Lyapunov exponents.