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Applied nonlinear dynamics

Applied Nonlinear Dynamics

Nonlinear dynamics and its applications at Leeds has for many years enjoyed reputation for a distinctive interdisciplinary approach. The Centre for Nonlinear Studies was established at Leeds in 1984 to enhance existing and foster new research collaborations between mathematicians, scientists and engineers throughout the University and beyond. Twenty five years later, the research group retains its character as an applications driven centre, and has recently expanded.

The Applied Nonlinear Dynamics group publishes the quarterly online newsletter UK Nonlinear News, and organizes weekly LAND (Leeds Applied Nonlinear Dynamics) seminars.

Research areas

The interests of the group range from core areas, such as chaos, global bifurcation theory and the role of symmetry, coupled oscillators and synchronisation, ergodic theory and stochastic dynamics, and pattern formation in fluid mechanics and reaction-diffusion systems, through to important areas of application, such as flame propagation, microfluidics, theoretical immunology and angiogenesis.

Whilst the research interests of the group are broad ranging they can be split into two broad categories.

Core nonlinear dynamics
Nonlinear dynamics is a fast-changing subject, and theory has to be developed quickly to keep up with progress in applications.  Many different aspects of the fundamentals of nonlinear dynamics are advanced at Leeds. Areas under current investigation include pattern formation and quasipatterns, the role of symmetry in dynamical systems, the ergodic theory of mixing, stochastic differential equations, global bifurcation theory and synchronisation.

Applications of nonlinear dynamics
In this large group, developments in the basic theory and techniques of Nonlinear Dynamics go hand-in-hand with investigations of particular applications. The AND group is particularly strong in the application area of chemical reaction-diffusion problems and flame propagation, and in mathematical biology: particularly gene regulation, theoretical immunology and viral dynamics, and angiogenesis, tumour invasion and morphogenesis.

For further information on our research please visit our Group pages