Spatio-Temporal Systems Estimation, Modelling and Analysis

任何一点的动态都依赖于过去的动态和邻近空间位置的动态的系统是普遍存在的。这些时空或时空系统代表了一大类高度复杂的动力系统，迄今为止的研究在很大程度上被忽视了。这是一个影响的邻居的空间相互作用，与时间动态结合在一起，产生复杂的相互作用行为的演变模式。现实生活中时空系统的例子很容易找到，范围从神经成像应用到干细胞和反应扩散系统。本研究的主要目标是推导出基于通用系统识别和参数估计的程序来识别这些复杂系统的模型，为这类模型开发模型验证方法，研究基于不变动态测量的特征，并将结果应用于一系列模拟和真实的时空系统。

Systems where the dynamics at any point depends upon the dynamics back in time and the dynamics at neighbouring spatial locations are ubiquitous. These space-time or spatio-temporal systems represent an enormous class of highly complex dynamical systems that have been largely ignored in studies to date. It is the spatial interactions over a neighbourhood of influence that together with the temporal dynamics combine to produce evolving patterns of complex interacting behaviours. Real life examples of spatio-temporal systems are easy to find and range from neuro-imaging applications to stem cells and reaction diffusion systems. The main objective of this research study will be to derive generic systems identification and parameter estimation based procedures to identify models of these complex systems, to develop model validation methods for this model class, to investigate characterisation based on invariant dynamic measures, and to apply the results to a range of both simulated and real spatio-temporal systems.