Mathematical modeling of evolving systems

Discover the multidisciplinary nature of the dynamical principles at the core of complexity science.

COURSE NUMBER: CAS 522
COURSE TITLE: Dynamical Systems
LEVEL: Graduate

SCHOOL: School of Complex Adaptive Systems
INSTRUCTOR: Enrico Borriello

MODE: Online
SEMESTER: Fall 2021
SESSION: Session B

DESCRIPTION
From physics and engineering to chemistry, biology, ecology and sociology. Mathematical modeling of evolving systems represents both a predictive tool and an interpretive lens through which complexity science uncovers the similarities shared by seemingly distant phenomena.

During this class the student will be presented with a wide variety of real-world dynamical systems, and learn the general tools and concepts used to model and predict their time evolution. This course will cover both the traditional approach to dynamical systems in terms of differential equations, as well as analytical and computational techniques for discrete systems. It will cover examples of both deterministic and stochastic dynamics, and focus on important nonlinear effects.

Through their assignments, the student will have a chance to give concrete meaning to abstract notions, and gain familiarity with powerful python libraries commonly used in the analysis of dynamical systems. No previous coding expertise is required, and each module will be complemented with tutorials on how to complete the numerical part of the assignments.

KEY WORDS
attractors, bifurcation, cellular automata, chaos, complexity, computational modeling, difference equations, differential equations, dynamical systems, gene regulatory networks, networks, nonlinear dynamics, python, stochastic processes