S-system modelling of complex systems with chaotic input

Environmental systems are characterized by large numbers of constituents and processes at hierarchical levels of organization. These levels range from elemental chemical and physical phenomena to multi-faceted ecosystems that are subject to natural and anthropogenic influences. The analysis of environmental systems is complicated because the governing processes are usually complex and ill defined. In addition to the structural complexity of the investigated phenomena themselves, environmental systems are difficult to analyze because they are constantly exposed to inputs that appear to fluctuate in a chaotic fashion. S-system models have the potential to address this situation. They are sets of nonlinear ordinary differential equations that were developed as representations for organizationally complex models, primarily in biology and biochemistry. They are characterized by a mathematical structure that allows efficient symbolic and numerical analysis of key features such as steady states, stabilities, sensitivities, and gains. At the same time, S-systems are structurally rich enough to capture virtually all relevant continuous nonlinearities. This paper begins with a brief review of two key features of S-systems: modelling and simulation based on power-law approximation; and the transformation method of recasting which allows differential equations to be formulated exactly as S-systems. The paper then discusses how chaotically fluctuating input can be simulated with a recast S-system based on deterministic chaos and how this recast S-system can be used as an input module for environmental phenomena that are represented as S-system models via power-law approximation.