APPROXIMATE METHOD FOR THE DETECTION OF CHAOTIC MOTION IN A TYPE OF DUFFING'S OSCILLATOR

摘要: The paper deals with the particular Duffing's oscillator x+0.2x+x+x3=Fcoswt. For F=50 and 1.5<ω<2.0 response was chaotic. Taking into consideration set of changes in ω case subharmonic resonances order 1 /2 1/3 ultraharmonic 2 3 have been considered. resonance, using harmonic balance method, non-linear algebraic equations were derived for relationship between amplitudes vibrations, amplitude exciting force F frequency ω, which solved numerically. Secondly, a different F, obtained, also method. Approximate solutions these found by Monte Carlo method then served as starting point Urabe's numerical technique to obtain close exact values unknown quantities. In all cases, it has shown that parameters at corresponding chaotic response, real vibrational either do not exist or are unstable.