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Imae, J., Furudate, T. and Sugawara, S. (1997) A Simple Numerical Method for Minimizing the Maximum Eigenvalues of Symmetric Matrices via Nonlinear Differential Equation Solvers. Transactions of the Japan Society of Mechanical Engineers, 63, 87-92.

has been cited by the following article:

• TITLE: A Method for Finding Optimal Parameter Values Using Bifurcation-Based Procedure

  AUTHORS: Hiroyuki Kitajima, Tetsuya Yoshinaga

  KEYWORDS: Bifurcation, Stability, Dynamical System

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.3 No.2, June 17, 2014

  ABSTRACT: In dynamical systems, the system suddenly becomes unstable due to parameter perturbation which corresponds to environmental changes or major incidents. To avoid such instabilities in engineering systems, tuning system parameters is very important. In this paper, we propose a method for obtaining optimal parameter values in a parameterized dynamical system. Here, the optimal value means the farthest point from the bifurcation curves in a bounded parameter plane. As illustrated examples, we show the results of continuous-time and discrete-time systems. Our algorithm can find the optimal parameter values in both systems.