**Autors:** Petrova, Z. A., Puleva, T. T.
**Title:** The mathematical modeling of the equation of Duffing with applications for master degree students-Part II (Open Access)
**Keywords:** Duffing equation, sufficient conditions for oscilation**Abstract:** All the parts of this publication treat different aspects of the qualitative theory of the Duffing equation ẍ(t)+δẋ(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 ẍ(t)+δẋ(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 ẍ(t)+δẋ(t)+αx(t)+βx3(t)=0 and make some connection with the bifurcation theory
**References**
**Issue**
| AIP Conference Proceedings. 45th International Conference on Application of Mathematics in Engineering and Economics, AMEE 2019; Sozopol; Bulgaria; 7 June 2019 through 13 June 2019, vol. 2172, pp. Article number 040006, 2019, Bulgaria, American Institute of Physics Inc., DOI 10.1063/1.5133516 |
Copyright American Institute of Physics Inc. |