Mathematical Sciences: Nonlinear Dynamical Systems in Mechanics and Biology

主要研究人员利用非线性动力系统技术对力学和生物学中的各种问题进行研究。这些主题包括流体系统中耗散偏微分方程的动力学和斑图的形成，对称系统的整体动力学，三维流动中的纽结和轨道谱系，具有缓变势的振子的动力学，神经生物振子的建模，一维映射的迭代，哈密顿系统和弱阻尼系统中的非线性稳定性和分叉。四维辛映射中的Arnold扩散，以及某些植物的生长动力学。这些主题在“智能”材料的设计和开发、航空航天(特别是卫星和航天器)、湍流边界层的控制以及生物学方面都有应用。

The principal investigators undertake studies of a variety of problems in mechanics and biology, using techniques of nonlinear dynamical systems. The topics include the dynamics of dissipative partial differential equations and pattern formation in fluid systems, global dynamics of symmetric systems, knots and orbit genealogy in three-dimensional flows, dynamics of oscillators with slowly varying potentials, modelling of neurobiological oscillators, iterations of one-dimensional mappings, nonlinear stability and bifurcation in Hamiltonian and weakly damped systems. Arnold diffusion in four-dimensional symplectic maps, and dynamics of the growth of certain plants. These topics have applications in the design and development of "smart" materials, in aerospace (particularly satellites and spacecraft), in the control of turbulent boundary layers,and in biology.