An approximate internal model principle: Applications to nonlinear models of biological systems

Abstract The proper function of many biological systems requires that external perturbations be detected, allowing the system to adapt to these environmental changes. It is now well established that this dual detection and adaptation requires that the system has an internal model in the feedback loop. In this paper we relax the requirement that the response of the system adapts perfectly, but instead allow regulation to within a neighborhood of zero. We show, in a nonlinear setting, that systems with the ability to detect input signals and approximately adapt require an approximate model of the input. We illustrate our results by analyzing a well-studied biological system. These results generalize previous work which treats the perfectly adapting case.

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