Chemical engineers have exploited nonlinear analysis of dynamical systems in diverse ways during the last century in the fields of chemical reaction engineering, fluid mechanics and transport processes. The objective of this presentation is to call attention to numerous topics in biological applications that represent opportunity areas for nonlinear analysis. The essential requirement of course is the availability of good dynamic models of such complex systems. While conservation principles and good constitutive supplements have proved sufficient for modeling of physical systems, biological systems add substantially to the challenge through features unique to them.

The unique features of biological systems are related to their capacity, acquired through exposure to eons of evolutionary pressures, to respond to their environment in ways that promote their survival. The consequence is an enormous increase in the diversity of responses of the system that modeling must necessarily represent within a dynamic framework. This requirement is enforced by the uncertainty surrounding our assessment of the organism's evolutionary experience that cannot be resolved without the institution of an interactive program of experiment and theory growing with contributions from each other. From this perspective, the opportunity in this area is not to be viewed simply as a Mecca for modelers for solely intellectual contentment. Rather, it will promote understanding of complex systems through the development of new experimental protocols that will provide a deeper setting for uncovering intriguing behavior. Some examples will be discussed.