Complexity, bifurcation and chaos in natural and man-made lumped and distributed systems

Complexity is a very diversified and branched subject and, ironically, is itself quite complex. In this paper, although we present the different aspects and definitions of complexity, we concentrate on its chemical/biological engineering relevance, especially for reaction/diffusion and hydrodynamic processes. System theory is used as the common language to unify concepts, and emphasis is given to bifurcation, chaos as the basis of behavioral complexity and the configuration of processes as the basis for structural complexity. Natural processes are grouped under biocomplexity, while man-made processes are treated as complexity alone. We restrict our attention in this paper to systems that do not change their structure during the process, so that self-organizational criticality is explained, but not utilized. Computational complexity is intrinsically inherent in all the processes we consider, but it is not given much attention in this paper. Despite these severe limitations on the scope of our paper, the subject is still quite complex and branched, and this paper tries to bring it to the attention and interest of a wider spectrum of chemical/biological engineers in both academia and industry.