Abstract
In this chapter, robust bifurcation analysis for nonlinear parameterized dynamical systems is introduced. It provides a direct method for finding the values of the system parameters at which the system has a steady-state with a high degree of stability using an optimization method. The approach is based on the idea of characterising the degree of stability as a function of the parameters. As a result, we could design a system that was robust to unexpected factors such as environmental changes and major incidents in applications. The optimization method is verified by using numerical experiments. An example of numerical results obtained in a model of the ventricular muscle cell suggests that our method can suppress the alternans and reduce the risk of sudden death.
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Acknowledgments
The proposed method of this research has been published as a paper in IJICIC [11] before. H.K. is partially supported by JSPS KAKENHI (No.23500367).
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Kitajima, H., Yoshinaga, T., Imura, Ji., Aihara, K. (2015). Robust Bifurcation Analysis Based on Degree of Stability. In: Aihara, K., Imura, Ji., Ueta, T. (eds) Analysis and Control of Complex Dynamical Systems. Mathematics for Industry, vol 7. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55013-6_2
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DOI: https://doi.org/10.1007/978-4-431-55013-6_2
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