Prediction and characterization of complex systems

摘要: Complex systems are difficult to characterize and simulate. By considering a series of explicit systems, through experiments analysis, this project has shown that dynamical can be used model complex systems. A system requires an exponential amount computer work simulate accurately. Direct methods not practical it is only by hierarchical approach one gain control over the behavior. This allows development efficient study fluid flow biological There two steps in approach. First, must as collection large domains or objects have their own forms interactions. done coherent structures, such solitons, spirals, propagating fronts determining Second, able predict properties resulting low-dimensional system.This accomplished understanding topology orbits system. The structure description was carried out reaction diffusion It very simple models from statistical mechanics could rotating Rayleigh-Benard patters reaction-diffusion well described soliton-like solutions. studies showed characterizations phase space determine long time bounds. Also, periodic orbit theory demonstrate Monte Carlo simulations will converge incorrect results.