Synthesis of a Nonlinear Dynamical System with a Number of Prescribed Closed Orbits and Singular Points as Its Limit Sets

Makoto ITOH  Tosiro KOGA  

IEICE TRANSACTIONS (1976-1990)   Vol.E65   No.6   pp.353-360
Publication Date: 1982/06/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Mathematics

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The inverse problem related to nonlinear dynamical systems has received considerable attention as a basic problem concerning the construction of oscillating systems. Recently, F. Gonzaléz-Gascon, F. Moreno-Insertis, and E. Rodriguez-Camino presented an open problem on the synthesis of a two-dimensional dynamical system. We present a complete solution to the above-mentioned problem. We synthesize a structurally stable dynamical system having prescribed points and simple closed curves of class C4 as its singular points and closed orbits respectively. As to the problem above, we clarify a topological constraint which is necessary for the above-mentioned dynamical system to be synthesize. In addition, an example of a dynamical system with three closed orbits is given.