For Better Performance Please Use Chrome or Firefox Web Browser

Delay Differential equations

  • Examples of delay differential equations(DDE), the simplest delay equations, Oscillation of Solutions
  • Existence, Uniqueness, Continuation of Solutions, Continuous dependence of Solutions on initial conditions and Parameters.
  • Stability theory, definitions, the method of Liapunov functionals, Liapunov functionals for authonomous systems.
  • Linear autonomous equations, the dynamical systems point of view, semiflows and omega limit sets, semidynamical systems induced by delay equations,
  • Strongly continuous semigroup, spectrum of generator, decompositions of C, characteristic matrices and equivalence, decomposing C with the adjoint equations,
  • Principle of linearized stability, hyperbolic and nonhyperbolic equilibrium points, hyperbolic periodic orbits, stable manifolds, unstable manifolds and center manifolds,
  • Introduction to theory of Hopf bifurcation for DDE, the center manifold reduction of DDE, approximation of local center manifold

References

  • Hale, J., Verduyn Lunel, S. Introduction to functional differential equations, Springer- verlag, 1993,
  • Smith, H., An introduction to delay differential equations with applications to life Sciences, Springer, 2011,
  • Arino, O., Hybid, M.L. and Ait Dads,E. Delay Differential equations and Applications, Springer, 2006,
  • Diekmann, o.. van Gils, S.A., Verduyn Lunel,S. M., Walther, H.O., Delay Equations, Functional- complex- and nonlinear Analysis, Springer-Verlag, New York, 1995.

 

Prerequisites: 
  • Dynamical systems I
  • Complex variables
  • Real Analysis
Grading Policy: 
  • Homeworks 40%
  • Seminar 30%
  • Final exam 30%
Time: 

Sunday-Tuesday 10-12am

Term: 
winter 2015
Grade: 
Graduate

تحت نظارت وف ایرانی