Prof. Sebastian Wieczorek

Chair and Head of Applied Mathematics

Chair and Head of Applied Mathematics

**Research Interests:**

Nonlinear Dynamics

Applied Bifurcation Theory

**Application Areas:**

Laser Dynamics

Tipping Points

Coupled Systems

**Address:**UCC, School of Mathematical Sciences,

Western Gateway Building G-49, Cork, Ireland

**Tel:**+353 (0)21 420 5828

**Email:**sebastian.wieczorek@ucc.ie

Examples of my research

**Stability diagram of coupled semiconductor lasers**

used in modern applications ranging

from communication schemes, to random

number generation, and medicine. As the

coupling between lasers increases (going

from bottom to top) their behaviour changes

from regular (yellow-red) to chaotic or

unpredictable (shades of grey). Complexity of

such transitions is aesthetically pleasing

but mathematically challenging.

SIAM J. Appl. Dyn. Syst. article

**Rate-induced tipping points**

describe the failure of a physical system to adapt

to changing external conditions. When external

conditions vary in time, the position of the

stable equilibrium "a" changes, and the system

tries to track the moving equilibrium. However,

if external conditions vary too fast, systems

will fail to track the moving equilibrium and

may suddenly go to another (undesired) state.

Mathematically, these are nonautonomous

instabilities that cannot, in general, be captured

by the traditional stability theory. Thus, they

require an alternative approach.

The example illustrates the compost-bomb

instability: a sudden and unexpected release of

soil carbon C from peatlands into the

atmosphere above some critical rate of warming.

This instability involves a nonobvious

threshold: (blue curve) a canard trajectory

through a folded saddle singularity "F".

CBS News article

Science daily article

Proc. Roy. Soc. A article

**Shear-induced chaos in perturbed lasers.**

Lasers are light amplifiers that consist of an

optical resonator filled with an active medium.

Parameter alpha, also known as the linewidth

enhancement factor, arises from the

dependence of the laser resonant frequency

on the number of excited electrons, N, in the

active medium. Mathematically, alpha quantifies

the amount of shear in the laser phase space

or amplitude-dependent frequency. (Right

panel) Non-zero shear about the lasing

solution (red limit cycle) gives rise to stretch-

and-fold action. This is similar to the action of

a horseshoe map---a hallmark of deterministic

chaos.

SPIE Newsroom article

DSWeb Magazine article