Nonlinear systems

Nonlinear systems are everywhere, from meteorology to biology, from chemistry to quantum mechanics,... They may exhibit amazing behaviors (e.g. strange attractors, chaotic trajectories,...) and have remained a tremendous topic of interest for the last decades.

Synchronization

From a mathematical point of view, synchronization is observed in networks of coupled dynamical systems. In the real world (especially the living world), synchronization is omnipresent and occurs in various situations. Nature exhibits a lot of interesting and amazing examples of perfect synchronization: asian fireflies flashing together, crickets that chirp in unison, synchronized applause of the crowd asking for an encore after a concert, groups of women whose menstrual periods become mutually synchronized, synchronous firings of pacemaker cells of the heart, spiking neurons in the brain, ...

Neural networks

The electrical activity of a single neuron can be modeled in a simple way. However, in our brain, all the neurons are connected in a complex way so that they form a broad network. The whole network is then considered as a (nonlinear) dynamical system of large dimension. Its global behavior (synchronization, periodic firings,...) may be theoretically studied thanks to system theory and model reduction.

Strange attractor in Lorenz system

Male fireflies flashing in unison (Malaysia)