Control of Complex Nonlinear Systems with Delay

This research addresses delay effects in nonlinear systems, which are ubiquitous in various fields of physics, chemistry, biology, engineering, and even in social and economic systems. They may arise as a result of processing times or due to the finite propagation speed of information between the constituents of a complex system. Time delay has two complementary, counterintuitive and almost contradictory facets. On the one hand, delay is able to induce instabilities, bifurcations of periodic and more complicated orbits, multi-stability and chaotic motion. On the other hand, it can suppress instabilities, stabilize unstable stationary or periodic states and may control complex chaotic dynamics. This thesis deals with both aspects, and presents novel fundamental results on the controllability of nonlinear dynamics by time-delayed feedback, as well as applications to lasers, hybrid-mechanical systems, and coupled neural systems.

This thesis deals with delay effects in nonlinear systems, which feature in various fields of physics, chemistry, biology, engineering, and even in social and economic systems. It covers both the instabilities arising from time delay and their suppression.

Conclusion. Abstract. Introduction. Time-Delayed Feedback Control.- Control of Steady States.- Refuting the Odd Number Limitation Theorem.- Control of Neutral Delay-Differential Equations.- Neural Systems.- Summary and Outlook.- List of Figures.- List of Tables.- Bibliography.- Acknowledgements- Index.