Title: Mathematical Theory for Complex Systems Modelling and its Applications in Science and Technology
Abstract:This talk will review our recent study on mathematical theory of complex systems modelling and its wide-ranging transdisciplinary applications in science and technology from the viewpoint of mathematical engineering and chaos engineering [1-3]. We aim not only to systematize methodology for mathematically modelling complex systems on the basis of complex networks theory, control theory of complex systems, and nonlinear time series analysis, but also to provide solutions for complex societal problems with high importance and urgency, such as mathematics-based personalized treatment for prostate cancer [4] and novel nonlinear electronic technology like chaos chips and AD converters based on β encoders [5].
References:
[1] K. Aihara(Ed.): Theme Issue on Theory of Hybrid Dynamical Systems and its Applications to Biological and Medical Systems, Philosophical Transactions of the Royal Society A, Vol.368, No.1930 (2010).
[2] L. Chen, R. Wang, C. Li, and K. Aihara: Modeling Biomolecular Networks in Cells: Structures and Dynamics, Springer, London (2010).
[3] G. Tanaka, K. Morino, and K. Aihara: Dynamical Robustness in Complex Networks: The Crucial Role of Low-degree Nodes, Scientific Reports, Vol.2, No.232, pp.1-6 (2012).
[4] Y. Hirata, G. Tanaka, N. Bruchovsky and Kazuyuki Aihara: Mathematically Modelling and Controlling Prostate Cancer under Intermittent Hormone Therapy, Asian Journal of Andrology, Vol.14, pp.270-277 (2012).
[5] T. Kohda, Y. Horio, Y. Takahashi, and K. Aihara: Beta Encoders: Symbolic Dynamics and Electronic Implementation, International Journal of Bifurcation and Chaos (in press).