The study of dynamical systems governed by partial differential equations (PDEs) offers profound insights into the evolution of complex phenomena across physics, biology and engineering. In these ...

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 ...

This new AI acts like a digital scientist, turning messy data into simple rules that explain how the world really works.

A new AI developed at Duke University can uncover simple, readable rules behind extremely complex systems. It studies how ...

We often encounter nonlinear dynamical systems that behave unpredictably, such as the earth's climate and the stock market. To analyze them, measurements taken over time are used to reconstruct the ...

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 ...

Earn an Online Dynamic Systems Certificate. Equip Yourself For Success in Model-Based Engineering. Our world is composed of dynamic systems: those that are not static but that change with time due to ...

This paper is a continuation of our study on doubly nonlinear parabolic type equations that was initiated by a previous paper; it is however self-contained. We propose here to investigate a time ...

Example-oriented survey of nonlinear dynamical systems, including chaos. Combines numerical exploration of differential equations describing physical problems with analytic methods and geometric ...

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 ...