Lucas Illing's homepage

Project ideas

Below are some details to give you an idea of what some of the projects are about. I have many more ideas - so come and see me.

  • Test KL-approach of data-analysis using numerics

    Compare Karhunen-Loève computation of entropy with comparable measures based on Lyapunov exponents. Do they give the same estimate of complexity?

    What is involved:
    Implement simulation of the model equations for the opto-electronic laser system using integrators for delay-differential equations that can handle stiff systems (RADAR5, try also dde23). Then develop an improved method for the calculation of Lyapunov exponents. Write code for Karhuen-Lowe decomposition of the space-time plot of the output of the improved integrator.

  • Broadband Chaos in Opto-Electronic Feedback Systems

    The main focus of the research project is to construct an opto-electronic device that has a bandwidth extending up to several GHz, characterize the system components, and explore regimes of operation of this device that have not been explored before. In particular, it has been found that by tuning the bias voltage of the Mach-Zehnder fiber-optic modulator the device exhibits chaotic dynamics characterized by a broad featureless spectrum filling the whole passband. We will conduct experiments to elucidate the dynamical origin of the observed behavior.

    What is involved:
    You will use state-of-the art measurement equipment such as broadband real-time oscilloscopes and spectrum analyzers to test the radio-frequency components. Once you understand how the system components work and the opto-electronic feedback device is assembled, the goal is to study the nonlinear device dynamics with a special focus on bifurcations leading from simple steady state behavior to periodic and more complex oscillations. Along the way you will be introduced to nonlinear time-series analysis techniques in order to analyze the data.

    Larger group `Chaotic Breathers in Delayed Electro-Optical Systems,' PRL (2005).

    Larger group `From Flow to Map in an Experimental High-Dimensional Electro-Optic Nonlinear Delay Oscillator', PRL (2005).

    Argyris+Occult project `Chaos-based communications at high bit rates using commercial fibre-optic links', Nature (2005).

  • The Dynamics of Coupled Systems with Delay (2008/2009)

    The aim of this research project is to construct, couple, and explore the dynamics of three opto-electronic devices. The initial focus will be on coupling the three devices in a linear array using mutual coupling. For laser with purely optical feedback such an experimental setup has yielded surprising behavior, such as isochronal chaos synchronization of the two outer lasers in the absence of isochronal synchronization to the laser in the middle. The origin of such synchronization via mediating oscillators is a currently active area of research. It is not known whether such behavior also occurs in opto-electronic time-delay systems with band-limited feedback, such as our systems.

    What is involved:
    This project requires the control and minimization of parameter differences between the three systems and the exploration of means to couple the systems. Both coupling through radio-frequency electrical signals and coupling via optical signals will be explored. Therefore this project will involve working with both radio-frequency components and fiber-optics.