Mathematical Sciences: Nonlinear Dynamical Systems in Mechanics and Biology

主要研究人员使用非线性动力系统技术，研究力学和生物学中的各种问题。主题包括耗散偏微分方程的动力学和流体系统的模式形成，对称系统的全局动力学，三维流动中的结和轨道谱系，具有缓慢变化电位的振荡器的动力学，神经生物学振荡器的建模，一维映射的迭代，哈密顿系统和弱阻尼系统的非线性稳定性和分岔。四维辛图中的阿诺德扩散，以及某些植物生长的动力学。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）、湍流边界层的控制和生物学中都有应用。

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.