Dynamical systems and differential equations form the backbone of many modern scientific and engineering endeavours, providing a robust mathematical framework to understand how complex phenomena ...

We show that any two trajectories of solutions of a one-dimensional fractional differential equation (FDE) either coincide or do not intersect each other. However, in the higher-dimensional case, two ...

The advent of big data coupled with advanced machine learning techniques has ushered in a new era in the discovery of dynamical systems and differential equations. This emerging interdisciplinary ...

Use individual and team exercises to build skills for a dynamic systems approach. Engineered systems increasingly must exploit complex interactions between multiple domains—mechanical, electrical, ...

homework sets (assigned roughly bi-weekly during the semester). class participation (extra points for helping me to make this class a lively one) projects (written project due at the end of the ...

Researchers at the University of Toronto have made a significant step towards enabling reliable predictions of complex dynamical systems when there are many uncertainties in the available data or ...

A research team has developed a novel method for estimating the predictability of complex dynamical systems. Their work, "Time-lagged recurrence: A data-driven method to estimate the predictability of ...

A system of equations where the output of one equation is part of the input for another. A simple version of a dynamical system is linear simultaneous equations. Non-linear simultaneous equations are ...

homework sets (assigned roughly bi-weekly during the semester). class participation (extra points for helping me to make this class a lively one) projects (written project due at the end of the ...