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Evaluation of circadian clock model based on orbital stability

The interactions among the components of biological systems, which are DNA, RNA and proteins, create specific cell functions. Recently, many works try to understand mechanism of the interactions from dynamical systems viewpoints, and for this problem, concepts and results in control engineering are expected to play significant role. However, the biological systems are generally nonlinear and complex, and are difficult objects of analysis and synthesis. In this paper, we propose an evaluation method, which is based on orbital stability analysis, of identifying important parts of nonlinear systems that have periodic orbits such as circadian rhythms or cell cycle control, and apply the method to a circadian rhythm model for Drosophila proposed by Leloup and Goldbeter (1998).