In the realm of nonlinear dynamics the whole is greater than or might even become very different from the sum of its parts leading to the emergence of novel and coherent structures or patterns. Such emergent entities have their own peculiar way of interacting, maybe on a higher level of description. For instance the molecules of chemistry emerge from nonlinear interactions on the atomic level that provide structures for proteins (and ribonucleic acids) of biochemistry and so on. The nonlinear interactions within a description level and the nonlinear interconnections of various such levels result in a whole which may (or may not) offer a hierarchical network structure. The choice of suitable order parameters and appropriate scaling is of utmost importance for the understanding (analysis, design and optimization) for each level and for the whole system.

For continuous processes, nonlinear dynamics addresses these choices in models given in terms of ordinary or partial differential equations, or differential-algebraic equations or population balance equations allowing tuning or control actions, often after state estimation/parameter identification.

At the MPI, nonlinear dynamics occur in the study of large scale systems like biochemical reaction networks or electrical circuits as well as in the analysis and design of smaller systems like the subunits/motifs arising in a modularization approach. Intensive work is dedicated to reliable model reduction techniques and semi-global approximation methods. Hereby, the interdisciplinary cooperation within the MPI has proven to be a fruitful basis for a successful development and implementation of such reduction strategies. The results, often non-local, for the reduced systems are then validated (numerically and experimentally). Other important questions in nonlinear dynamics, like stability, bifurcation and sensitivity analysis and robustness margins are studied for various challenging application examples.