Patrick Tchepmo Djomegni
Summary: Most real-world problems and the fundamental laws of physics are formulated in terms of
differenal (oen nonlinear) or difference equaons (DEs). Despite significant advances in analycal
techniques, the majority of nonlinear DEs do not admit explicit soluons. This course is devoted to
the analysis of connuous-me dynamical systems, with an emphasis on qualitave rather than
quantave methods. In parcular, the module examines system stability and sensivity to small
perturbaons.
Upon compleon of this module, students will be able to idenfy and interpret equilibrium points
and their physical significance; analyze local and global stability properes of equilibria; understand
and interpret the concepts of bifurcaons and limit cycles; and numerically construct and interpret
phase portraits, vector fields, and soluon trajectories.
Successful compleon of the module will equip students with the theorecal and praccal tools
necessary to analyze the qualitave behavior of systems governed by differenal equaons.
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.