Métodos especiales para el estudio de dinámica global de sistemas caóticos / Special methods for study of global dynamics of chaotic systems
Clave: 11B6390
No. de horas: 72
Créditos: 5
Tipo de asignatura: Optativa
Fecha de elaboración: 2016-01-29
Objetivo general:
- Provide tools for analyzing dynamics of chaotic systems.
- Provide the basic concepts of linear systems.
- Provide basic concepts and mathematical tool for the analysis of local stability of nonlinear systems.
- Provide basic concepts and mathematical tools for the analysis of global stability and localization of compact invariant sets of nonlinear systems.
- Examples of global dynamics study of some nonlinear systems in physics.
- Examples of global dynamics study of some nonlinear systems in mathematics medicine.
Temas:
- Linear systems.
- Analysis of local stability of nonlinear systems.
- Elements of global dynamics.
- Examples of study of global dynamics of some nonlinear physical systems.
- Global analysis of tumor growth models under therapy.
Bibliografía:
- H. Khalil, Nonlinear systems.Prentice Hall, 2002. (AII units).
- L. Perko, Differential Equations and Dynamical System, Springer 1996, Texts in Applied Mathematics (Units 1, 2 and3).
- V.A. Boichenko, G.A. Leonov, V. Reitmann,Dimension Theory for Ordinary Differential Equations, Teubner 2005 (Unit 2).
- J. Guckenheimer, P. Holmes,Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields,Springer 2002 (Units 1, 2, 3 and 4).
- A. Krishchenko, K.E. Starkov,Localization of compact invariant sets of nonlinear time-varying systems,International Journal of Bifurcation and Chaos, 18, N 5, pp. 1599-1604,2008(Unit 3).
- A. Krishchenko, K.E. Starkov,Localization of compact invariant sets of the Lorenz system, Physics Letters A,2006, 353, pp.383-388 (Unit 4).
- K.E. Starkov, Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems,Physics Letters A, 372, pp. 6269-6272, 2008 (Unit 4).
- K.E. Starkov, Bounds for compact invariant sets of the system describing dynamics of the nuclear spin generator,Communications in Nonlinear Science and Numerical Simulation, 14, pp.2565-2570, 2009 (Unit 4).
- K.E. Starkov, Compact invariant sets of the statics pherically symmetric Einstein -Yang-Mills equations, Physics Letters A, 374,pp. 1728-1731,2010 (Unit 4).
- K.E. Starkov, Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems, Physics Letters A, 375, pp.3184-3187, 2011 (Unit 4).
- K.E. Starkov, Unbounded dynamics and compact invariant sets of one Hamiltonian system defined by the minimally coupled field, Physics Letters A, 379, pp.11012-1016,2015 (Unit 4).
- K.E. Starkov, Periodic orbits and 10 cases of unbounded dynamics for one Hamiltonian system defined by the conformally coupled field,Physics Letters A, 379, pp. 1337-1341, 2015 (Unit 4).
- K.E. Starkov, L. Coria, Global dynamics of theKirshner- Panetta model for the tumor immunotherapy, Nonlinear Analysis: Real World Applications, 14, pp. 11425-1433,2013 (Unit 5).
- K.E. Starkov, A.P. Krishchenko, On the global dynamics of one cancer tumor growth model, Communications in Nonlinear Scienceand Numerical Simulation, 119, pp. 1486-1495,2014 (Unit 5).
- K.E. Starkov, D. Gamboa, Localization of compact invariant sets and global stability in analysis of one tumor growth model, Mathematical Methods in the Applied Sciences, 37, pp. 2854-2863, 2014(Unit 5).