Center for Nonlinear and Complex Systems

The Center for Nonlinear and Complex Systems (CNCS) fosters research and teaching of nonlinear dynamics and the mechanisms governing emergent phenomena in complex systems. The CNCS at Duke is widely recognized for the breadth of its activities and the overall quality of the research which it engenders. The Center provides a research seminar series and a Graduate Certificate Program, as well as numerous opportunities for undergraduate and graduate research through its associated faculty.

Graduate Certificate in Nonlinear and Complex Systems

The purpose of the certificate is to broaden the scope of the typical disciplinary; graduate student traning program. Students are encouraged to develop interdisciplinary; and transferable sets of skills in their course work and research activities. The certificate program helps to guide students toward this broad view by  requiring the completion of:

  • The seminar course
  • Four courses from the approved list (below)
  • A Ph.D. dissertation on a topic in the domain of the CNCS

In addition, the student must have two members of the Center on their Ph.D. dissertation committee. Students are encouraged to meet together with their dissertation thesis advisor and the Associate Director of the Center (Prof. L. Virgin) early in their graduate studies to help with course planning and dissertation committee selection.

Physics (PHYSICS)

320. Optics and Photonics
513. Introductory Nonlinear Dynamics
562. Fundamentals of Electromagnetism
563. Introduction to Statistical Mechanics
621. Advanced Optics
719. Advanced Electrodynamics
760. Mathematical Methods in Physics
761. Classical Mechanics
763. Statistical Mechanics
804. Advanced Topics in Statistical Mechanics
813. Advanced Topics in Nonlinear and Complex Systems
814. Introduction to Fluid Mechanics

Mechanical Engineering and Materials Science (ME)

307. Transport Phenomena in Biological Systems
519. Soft Wet Materials and Interfaces
525. Nonlinear Finite Element Analysis
527. Buckling of Engineering Structures
531. Engineering Thermodynamics
532. Convective Heat Transfer
536. Compressible Fluid Flow
541. Intermediate Dynamics: Dynamics of Very High Dimensional Systems
542. Modern Control and Dynamical Systems
543. Energy Flow and Wave Propagation in Elastic Solids
544. Advanced Mechanical Vibrations
546. Intelligent Systems
571. Aerodynamics
572. Engineering Acoustics
631. Intermediate Fluid Mechanics
632. Advanced Fluid Mechanics
639. Computational Fluid Dynamics and Heat Transfer
643. Adaptive Structures
671. Advanced Aerodynamics
672. Unsteady Aerodynamics
741. Nonlinear Control Systems
742. Nonlinear Mechanical Vibration
775. Aeroelasticity

Biomedical Engineering (BME)

301. Electrophysiology
307. Transport Phenomena in Biological Systems
506. Measurement and Control of Cardiac Electrical Events
512. Theoretical Electrocardiology
513. Nonlinear Dynamics in Electrophysiology
516. Computational Methods in Biomedical Engineering
531. Intermediate Biomechanics
566. Transport Phenomena in Cells and Organs
834. Viscoelasticity

Civil and Environmental Engineering (CEE)

307. Transport Phenomena in Biological Systems
520. Continuum Mechanics
541. Structural Dynamics 581. Pollutant Transport Systems
621. Plasticity
625. Intermediate Dynamics
630. Nonlinear Finite Element Analysis
641. Advanced Soil Mechanics
647. Buckling of Engineering Structures
648. Multivariable Control
682. Dynamic Engineering Hydrology
690. Advanced Topics in Civil and Environmental Engineering

Mathematics (MATH)

451S. Nonlinear Ordinary Differential Equations
541. Applied Stochastic Processes
545. Introduction to Stochastic Calculus
551. Applied Partial Differential Equations and Complex Variables
553. Asymptotic and Perturbation Methods
555. Ordinary Differential Equations
557. Introduction to Partial Differential Equations
561. Numerical Linear Algebra, Optimization and Monte Carlo Simulation
563. Applied Computational Analysis
573S. Modeling of Biological Systems
575. Mathematical Fluid Dynamics
577. Mathematical Modeling
641. Probability
651. Hyperbolic Partial Differential Equations
653. Elliptic Partial Differential Equations 660. Introduction to Numerical PDEs
661. Numerical Solution of Hyperbolic Partial Differential Equations
663. Numerical Solution of Elliptic and Parabolic Partial Differential Equations


268. Ecological Theory and Data
291. Mathematical Biology
292. Population Ecology
293. Simulating Ecological and Evolutionary Systems
303. Principles of Ecological Modeling
304. Plant Growth Modeling

Computer Science

240. Computational Complexity 
250. Numerical Analysis 
252. Numerical Methods for Partial Differential Equations
264. Nonlinear Dynamics 
270. Artificial Intelligence 
271. Numerical Artificial Intelligence
350. Topics in Numerical Mathematics
364. Advanced Topics in Nonlinear and Complex Systems 

Earth and Ocean Sciences

203. Physical Oceanography
207. Analysis of Coastal Engineering Models
221. Hydrogeology
222. New Perspectives and Methods in the Earth Sciences
223. Computational Methods in Hydrologic Sciences
230. Advanced Structural Geology
250. Applied Mathematics for the Environmental and Earth Sciences
252. Geophysics and Crustal Dynamics

Electrical and Computer Engineering

241. Linear Systems: Theory and Control
243. Pattern Classification and Recognition
255. Mathematical Modeling for Systems Analysis I
258. Artificial Neural Networks
263. Multivariable Control
281. Random Signals and Noise
282. Digital Signal Processing
285. Signal Detection and Extraction Theory
288. Image and Array Signal Processing
289. Adaptive Filters
299. Nonlinear Control Systems (Advanced Topics)

School of the Environment

216. Applied Population Ecology
290. Physical Oceanography
356. Environmental Fluid Mechanics



The only formal paperwork that must be completed to obtain the certificate occurs when the student's Ph.D. dissertation is submitted to the Graduate School.&nbsp; The student should check the box on the Graduate School "<a href="">Intent  to Receive Degree Form</a>" indicating that they would like to receive the  CNCS Graduate Certificate. The student must then send the Associate Director of the Center   the following information:

  • the semester(s) when CNS 201 was taken
  • the name of the four courses taken (from the approved list
  • the Ph.D. dissertation title
  • the list of final Ph.D. dissertation committee members
  • the date of the final defense
  • the final Ph.D. dissertation abstract
  • the student's graduate transcript

Biomedical Engineering
Civil Engineering
Computer Science
Earth and Ocean Sciences
Electrical Engineering
Mechanical Engineering and Materials Science
School of the Environment