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 ...

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 ...

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 ...

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems. Joseph Silverman remembers when he began connecting ...

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 ...

Duke University engineers are using artificial intelligence to do something scientists have chased for centuries; turn messy, real-world motion into simple rules you can write down. The work comes ...

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 ...

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 ...