The Chemical Engineering Department is hosting a special undergraduate lecture about Linear stability analysis.
In this lecture, the Jacobian matrix will be introduced as a tool to characterize steady-state solutions to systems of coupled ordinary differential equations (ODEs). First, the theoretical basis for the relationship between matrix eigenvalues and system dynamics will be developed. Then methods, including computational approaches, to find eigenvalues will be briefly reviewed using examples relevant to chemical and biological engineering problems. Geometric and dynamic interpretations to control analysis and engineering will be briefly discussed. Finally, the stability constraints for some representative complex biological systems will be briefly explored using linear stability analysis. Participants will leagve this lecture with a solid framework for predicting the stability of dynamic systems using the Jacobian matrix, and knowledge of the more advanced tools available to them to evaluate the stability of larger more complex systems.
200 University Ave West
Waterloo, ON N2L 3G1