Abstract
For critical values of a bifurcation parameter a dynamical system can display Hopf bifurcation points. The detection of Hopf bifurcation points can be made using a continuation method -by calculation of the eigenvalues of the linearized system — or using a direct method. We examine herein this last opportunity. The direct method chosen is an optimization method, which main advantage is to use a set of parameters rather than one parameter.
The second part of this work is concerned with the application of a continuation method to the optimization of multistate systems. The two examples chosen are: the control of the amplitude of a periodic solution, the control of a period doubling point in a prey-predator model.
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© 1988 Springer-Verlag
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Trubuil, A. (1988). Hopf bifurcation point detection. application of a continuation method to optimization of multistate systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042296
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DOI: https://doi.org/10.1007/BFb0042296
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