Lecturer: PATRICK MIMPHIS TCHEPMO DJOMEGNI
Abstract
Most real-world problems and the fundamental laws of physics are formulated in terms of differential (often nonlinear) or difference equations (DEs). Despite significant advances in analytical techniques, the majority of nonlinear DEs do not admit explicit solutions. This course is devoted to the analysis of continuous-time dynamical systems, with an emphasis on qualitative rather than quantitative methods. In particular, the module examines system stability and sensitivity to small perturbations.
Upon completion of this module, students will be able to identify and interpret equilibrium points and their physical significance; analyze local and global stability properties of equilibria; understand and interpret the concepts of bifurcations and limit cycles; and numerically construct and interpret phase portraits, vector fields, and solution trajectories.
Successful completion of the module will equip students with the theoretical and practical tools necessary to analyze the qualitative behavior of systems governed by differential equations. Students will also develop mastery of core proof techniques and will be able to apply these methods to problems arising in biology, physics, economics, chemistry, astrophysics, and related disciplines.