| Abstract [eng] |
The Duffing equation is a non-linear second-order differential equation. It is an example of a dynamical system that exhibits chaotic behavior. In my final degree project we have investigated Duffing‘s equation with initial conditions and researched synchrony of solutions. A special program was created, it solves deteminated problem in t time range and finds the difference between answers. Depending on results, this program was modified in order to get the results needed. In first part we have looked at Duffing equation‘s answers and their difference. Numeric modeling results were studied using graphs. Parameters were chosen for all results be converged to one solution only. As well, we studied their convergence depending on those parameters. In the second part, we were interested in the time period when results match. The third part was dedicated to Duffing‘s equation, when and . We found periods for our solutions and researched their energy. Law of the energy conservation was double-checked as well. |
