CHAOTISCHE LÖSUNGEN BEI DER DREIFACHEN FREQUENZTEILUNG

Abstract

The paper deals with the solution of the model equation for threefold frequency distribution [1] t~ -{I-x:_(~:;YJ:~ +x+h(4xJ-3x)=Bcos3, (1) depending on the equation parameters ε, b and B. The mapping method appears particularly suited in the analysis on non-linear externally excited networks [2] [3]. By means of this stroboscopic method one succeeds to present a clear picture of the different solution structures in the different parameter ranges. Particular attention was paid to bifurcation characterized by qualitative changes in the periodical states and to chaotical solutions. Such stochastic movements will be observed in certain cases precisely in defined systems represented as in the present case by simple differential equations.