Physique Non-linéaire

Nonlinear Physics

Description: Physical systems in general are called dynamic because the state variables that characterize the state of these systems evolve in time and space when the parameters influencing these systems vary. When the dynamic relationships that link the state variables are non-linear functions of the state variables, the physical system is called a non-linear system. The non-linearity of these systems is at the origin of a great richness of their dynamic behaviors and allows the observation of new phenomena that interest scientists and engineers. Examples of non-linear dynamic systems include neural networks, electronic and optical oscillators, the dynamics of data propagation in a telecommunications network or the propagation of a virus. The most spectacular nonlinear dynamics are chaos - or the dynamics of a system that over time or while propagating presents an unpredictable evolution of its state variables - but also synchronization which allows two or more coupled nonlinear dynamic systems to reproduce the same dynamics, even chaotic. How the dynamics of a nonlinear system becomes complex and chaotic, and how this dynamic propagates between coupled oscillators in networks, are all fundamental questions but which also shed light on important fields of science and engineering such as neuroscience, artificial intelligence, telecommunications, epidemiology, quantum systems, etc. This course will therefore give the student the basic elements of what is more generally called nonlinear physics. It will be illustrated by numerous concrete cases taken from research work with an applied aim, which will allow the student to understand and implement the analytical and numerical techniques necessary for solving simple problems.

Bibliography:

• Ref. [1] : S. Strogatz, Nonlinear dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, CRC Press (2014)

Learning outcomes: By the end of this course, students will be able to: AA1: Understand the scientific and multidisciplinary challenges of nonlinear science and network theory – AA2: Identify situations where the formalism of nonlinear physics can be applied – AA3: Know and apply techniques for analyzing nonlinear dynamical systems and networks of oscillators – AA4: Perform numerical simulations of nonlinear dynamical systems and dynamic networks

Evaluation methods: Mini project

Evaluated skills:

• Physical Modeling

Course supervisor:

• Marc Sciamanna

Geode ID: SPM-PHY-006