Universiteit Leiden

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A fixed point approach towards stability of delay differential equations with applications to neural networks

Promotor: S.M. Verduyn Lunel, Co-Promotor: O.W. van Gaans

Guiling Chen
29 augustus 2013
Thesis in Leiden Repository

This thesis studies asymptotic behavior and stability of determinsitic and stochastic delay differential equations. The approach used in this thesis is based on fixed point theory, which does not resort to any Liapunov function or Liapunov functional. The main contribution of this thesis is to study the approach using fixed point theory in a systematic way and to unify recent results in the literature by considering some general classes of equations. The equation we considered is a combination of time dependent delays, distributed delays, impulses and stochastic perturbations. In addition, an application to stochastic delayed neural networks is investigated. The results in this thesis extend and improve some exist results in the literature in some ways. Examples are discussed in each chapter to illustrate our main results.