| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 758430 | Communications in Nonlinear Science and Numerical Simulation | 2013 | 8 Pages |
•The global properties such as attractors, basins of attraction, saddles are obtained.•Boundary and interior crises in an elastic impact oscillator are presented.•The vivid evolutionary process of crisis phenomena is described.•We find the composite cell coordinate system method is efficient in non-smooth system.
The crisis phenomena of a Duffing–Van der Pol oscillator with a one-side elastic constraint are studied by the composite cell coordinate system method in this paper. By computing the global properties such as attractors, basins of attraction and saddles, the vivid evolutionary process of two kinds of crises: boundary crisis and interior crisis are shown. The boundary crisis is resulted by the collision of a chaotic attractor and a periodic saddle on the basin boundary. It is observed that there are two types of interior crises. One is caused by the collision of a chaotic attractor and a chaotic saddle within the interior of basin of attraction. The other one occurs because a period attractor collides with a chaotic saddle within the interior of basin of attraction. The saddles of system play an important role in the crisis process. The results show that this method is an efficient tool to perform the global analysis of elastic impact oscillators.
