Abstract
MatContM is a MATLAB interactive toolbox for the numerical study of iterated
smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclitic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, tracing out solution manifolds 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 computational routines and functionalities, as well as a graphical user interface, enabling interactive control of all computations, data handling and archiving. 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.
smooth maps, their Lyapunov exponents, fixed points, and periodic, homoclinic and heteroclitic orbits as well as their stable and unstable invariant manifolds. The bifurcation analysis is based on continuation methods, tracing out solution manifolds 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 computational routines and functionalities, as well as a graphical user interface, enabling interactive control of all computations, data handling and archiving. 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.
Original language | English |
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Title of host publication | Journal of Physics |
Subtitle of host publication | Conference Series |
Publisher | IOP Publishing |
Volume | 692 |
DOIs | |
Publication status | Published - 2016 |
Event | NOMA’15 International Workshop on Nonlinear Maps and Applications - University College Dublin Belfield, Dublin, Ireland Duration: 15 Jun 2015 → … |
Conference
Conference | NOMA’15 International Workshop on Nonlinear Maps and Applications |
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Country/Territory | Ireland |
City | Dublin |
Period | 15/06/15 → … |