Your chances to get your PhD application accepted are higher if you get a potential supervisor to endorse your Research Proposal. You can also prepare a brief Research Proposal for application, if it is allowed.

The field of Dynamical Systems in Applied Maths is young. However, you can write about recent advances in Dynamical Systems & Applications. Then you identify an area of research interest and focus your attention on a particular system, namely Time-Delay Systems, Nonlinear Systems, Infinite Dimensional Systems, or Stochastic Systems. Your proposed study should make several substantial and original contributions to knowledge for deepening our understanding in Dynamical Systems. Your research should aim to answer the unsolved issues that are inspired by the literature review.

This post has been edited by Critical_Fallacy: Apr 16 2014, 01:34 AM

You should look for supervisors who have built up their authorities in the field of Epidemiology or Bifurcation theory (mathematics). There are some LYN users (v1n0d, ninty, jonoave, and LoveMeNot) whom I know maybe can guide you appropriately.