Nonlinear and Complex Systems

How does a network of interacting genes produce viable cells? Why does flowing sand sometimes get jammed in a static state? How do networks of neurons in the brain process information? How can coupling many simple sensors produce a network that outperforms traditional approaches?  What types of spatial and temporal patterns can arise in collections of many interacting elements?  Questions like these require research into the subtle origins of familiar natural phenomena, which in turn reveals new possibilities for achieving functions in evolved or engineered systems. The challenge is to discover and characterize the collective behavior of complex systems, and to uncover the principles that connect the physics and logic of interactions between individual parts to the properties of the full system. This rapidly developing research area relies heavily on the concepts and language of nonlinear dynamics, and research in this area at Duke began in the 1980's when physicists, geophysicists, mathematicians, and engineers recognized that they shared a common language.  Current efforts now extend also to collaborations with biologists and neuroscientists.

Experiments in these areas are typically carried out by individual students who have the opportunity to explore all aspects of a project, including design, construction, and data analysis. Theoretical progress relies on the adaptation and extension of principles of dynamical systems theory and statistical mechanics, distilling the crucial features of the system into models that can be studied analytically or using manageable numerical computations.

The Center for Nonlinear and Complex Systems (CNCS)

CNCS is an interdisciplinary University-wide organization that fosters research and teaching of nonlinear dynamics, chaos, pattern formation and complex nonlinear systems with many degrees of freedom. A number of physics faculty, post-docs and students actively participate in the Center. Other academic units with ties to the CNCS include the departments of Computer Science, Geology, and Mathematics, the Nicholas School of Environment and the Pratt School of Engineering. The CNCS sponsors a regular seminar series and a certificate program of study for graduate and advanced undergraduate students. Details may be found on the CNCS website.

Physics Faculty Home Pages (Primary department)


Experiments and modeling of soft matter systems: granular flows and jamming, granular impacts, fluid flows and instabilities. 


Theory of the evolution and function of biological oscillators; experiments on synthetic biological oscillators. (Biology)


Theory of glass formation; structure of colloidal systems and microphases; protein-protein interactions. (Chemistry)


Experiments on complex autonomous Boolean networks; self-organized behavior, information flow in networks and reservoir computing.


Theory and simulations of spatiotemporal patterns in fluids; neuronal activity associated with bird song and olfaction.

Jian-Guo Liu:

Applied mathematics, nonlinear dynamics, complex system, fluid dynamics, computational sciences  


Theoretical models of learning and memory in neural networks; glassy dynamics in random systems with frustrated interactions.  


Theory of network dynamics; models of gene regulatory networks; structure in colloidal systems; tiling theory and nonperiodic order.


Experiments on nonlinear dynamics of currents in semiconductors.