posterDynamical systems theory describes qualitative and quantitative features of solutions of systems of nonlinear differential equations, typically modelling processes which evolve over time. The theory has diverse roots in applications such as Poincaré’s work on planetary motion in the 19th century, the Fermi-Pasta-Ulam simulations of anharmonic lattices in the 1950s, and the famous Lorenz equations dating to 1963, which originated as a highly simplified model of Rayleigh-Benard convection. A deep and beautiful theory of nonlinear dynamical systems has resulted. However, dynamical systems which arise in practice are often outside the scope of much of this theory, either because they contain generalisations to the dynamical systems paradigm, such as variable or state dependent delays or even advanced arguments, or because assumptions or conditions within the theory do not apply.  An example of this is in the field of chaotic dynamics where much early work depended on the assumption of uniform hyperbolicity.  Unfortunately even the Lorenz equations, one of the simplest and most studied systems of equations exhibiting chaotic behaviour, do not have this property.  As a consequence it was only as recently as 2002 that Tucker established that the system does have a strange attractor.  Tucker’s proof required the use of validated interval arithmetic, and the use of numerical techniques is a common thread throughout the study of dynamical systems.


Despite the difficulties, significant progress has been made in recent years in applying dynamical systems particularly in the areas of mathematical biology and physiology. This has led to an increasing interest in new problems such as those with non-constant and distributed delays, which has given rise to new analytical and numerical challenges. Thus we choose to focus on two themes in this thematic semester. Firstly, the use of dynamical systems in applications, principally in physiology, and secondly the development of new numerical and dynamical systems tools needed in the study of such problems. These two broad themes will be addressed through a series of workshops and courses. However, applied dynamical systems is too vast a field to cover completely in a single semester, and we will not attempt to do so. Workshops on Mathematical Neuroscience and Biochemical networks will address physiological applications of dynamical systems, while workshops on Algorithms for Bifurcation Analysis and Functional Differential Equations will cover numerical techniques for dynamical systems, and the workshops on Functional Differential Equations and Hamiltonian Systems will address theoretical issues of applied dynamical systems. However, in reality applications, analysis and numerical methods are all interconnected and some aspects of all three will be found in each of the workshops. The workshops will bring together established stars as well as junior faculty and researchers in an environment where latest research results can be exchanged, but a significant feature will be the provision of free time for interaction and discussion, which we hope will seed new research projects. We are particularly keen to encourage participation of senior graduate students, postdoctoral fellows and junior faculty; workshop organisers include junior and mid-career faculty, and there will also be short and advanced courses targeted towards graduate students.