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| BIFURCATION ANALYSIS OF A CLASS OF PLANAR PIECEWISE SMOOTH LINEAR-QUADRATIC SYSTEM |
| Qiwen Xiu,Dingheng Pi |
| (Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, Fujian, PR China) |
| DOI： |
| Abstract: |
| In this paper, we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system. The quadra- tic system has some folds on the discontinuity line. The linear system may have a focus, saddle or node. Our results show that this piecewise smooth differential system will have two limit cycles and a sliding cycle. Moreover, this piecewise smooth system will undergo pseudo-homoclinic bifurcation, Hopf bifurcation and critical crossing bifurcation $CC$. Some examples are given to illustrate our results. |
| Key words: piecewise smooth systems;limit cycle; sliding cycle; pseudo-homoclinic bifurcation; critical crossing bifurcation $CC$ |