Intellectual Merit: The PI plans to develop systematic methodologies for engineering complex collective dynamic behavior that arises in chemical and biological systems composed of many interacting elements. Unlike approaches that focus on individual components of a system, the model-based approach describes emergent collective properties that cannot be understood only from a knowledge of the parts. Simplified yet accurate models of reduced order that nevertheless capture important features of system behavior are developed; these reduced models shall be derived directly from experiments and formulated without the need for mechanistic details on reaction kinetics. He will investigate the use of nonlinear feedback constructed with the help of experiment-based models in designing complex dynamic structure and tuning a wide spectrum of emergent collective behavior in systems composed of many elements. Since the feedback design methodology relies on a phase model description that describes general self-organized rhythmic patterns with weak interactions, the proposed methodology is capable of creating a large class of structures in weakly coupled systems. An important aspect of the proposed study is our ability to test the limits of applicability of the feedback methodology in independent experiments on populations of electrochemical oscillators in which the local dynamics and resulting waveform as well as the coupling strength and topology are systematically varied. Application will be made to mutual entrainment and dynamical differentiation, to the generation of sequentially visited dynamic cluster patterns, and to the design of nonlinear anti-pacemakers for the destruction of undesired synchronization of populations of interacting oscillators. He will address a question of both theoretical and practical importance: how to bring dynamical systems to a desired condition with weak, non-destructive signals without destroying the inherent local behavior.
Broader Impacts: The research addresses fundamental issues that are driven by practical applications of commercial importance. The study on experiment-based models will open a route to modeling, predicting, and controlling dynamic behavior in a large class of chemical and biological systems in which a quantitative description is required but where kinetic information is difficult to obtain. As such it could find application in reacting systems from chemical reactors to corrosion where interactions among reaction sites are dominant features of behavior. The general methodology being developed should be a valuable tool in a contemporary problem of systems engineering and systems biology, viz., what types of modeling and experimental tools are optimal in describing a hierarchy of interactions among large numbers of elements that are both mathematically tractable but yet which capture the essential properties of the system. It may help reveal how sub-cellular, cellular, tissue and system-level mechanisms collectively lead to synchronization, generation, and expression of physiological dynamical activities. The model-engineered feedback may find use in pacemaker and anti-pacemaker design for medical use (tremors, epilepsy) as well as for applications such as high-power lasers and microwave oscillators for communications.
A strong emphasis of the PI's studies is on the training of students and broadening the participation of underrepresented groups. Presently two female graduate students and two female undergraduate students are in our group; in the past ten years three African-American graduate students have completed their PhD studies. He will carry out collaborative studies and an active exchange of graduate students with international partners in Germany, China, Mexico, Japan, and Lithuania. He plans to continue his participation in presentation of his work in the USA and overseas; this includes workshops organized for students and investigators from third world countries.
