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
Unidades de crédito:  8
Créditos SATCA:  5
Tipo de asignatura: Optativa
Fecha de elaboración: 2016-01-29

Objetivo general:
  1. Provide tools for analyzing dynamics of chaotic systems.
  2. Provide the basic concepts of linear systems.
  3. Provide basic concepts and mathematical tool for the analysis of local stability of nonlinear systems.
  4. Provide basic concepts and mathematical tools for the analysis of global stability and localization of compact invariant sets of nonlinear systems.
  5. Examples of global dynamics study of some nonlinear systems in physics.
  6. Examples of global dynamics study of some nonlinear systems in mathematics medicine.

Temas:
  1. Linear systems.
  2. Analysis of local stability of nonlinear systems.
  3. Elements of global dynamics.
  4. Examples of study of global dynamics of some nonlinear physical systems.
  5. Global analysis of tumor growth models under therapy.

Bibliografía:
  1. H. Khalil, Nonlinear systems.Prentice Hall, 2002. (AII units).
  2. L. Perko, Differential Equations and Dynamical System, Springer 1996, Texts in Applied Mathematics (Units 1, 2 and3).
  3. V.A. Boichenko, G.A. Leonov, V. Reitmann,Dimension Theory for Ordinary Differential Equations, Teubner 2005 (Unit 2).
  4. J. Guckenheimer, P. Holmes,Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields,Springer 2002 (Units 1, 2, 3 and 4).
  5. 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).
  6. A. Krishchenko, K.E. Starkov,Localization of compact invariant sets of the Lorenz system, Physics Letters A,2006, 353, pp.383-388 (Unit 4).
  7. 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).
  8. 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).
  9. 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).
  10. 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).
  11. 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).
  12. 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).
  13. 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).
  14. 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).
  15. 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).