| Popis: |
All the parts of this publication treat different aspects of the qualitative theory of the Duffing equation x¨(t)+δx˙(t)+αx(t)+βx3(t)=u(t), where the coefficients α, β and δ are real constants and u(t)∈C([0,∞);R). In the first part we formulated sufficient conditions for oscillation for this equation assuming that α>0,β>0,δ∈Rand4α>δ2. We applied Matlab and Simulink for the linear particular case of the above equation, i. e. for x¨(t)+δx˙(t)+αx(t)=u(t) in order to illustrate the respective oscillation results.In this part we repeat only these sufficient conditions for oscillation, which are concerned with the following homogenous particular case of the Duffing equation x¨(t)+δx˙(t)+αx(t)+βx3(t)=0 and make some connection with the bifurcation theory. |
