are the trajectory of the system (5.69) with initial value (0 . 4 , 0 . 05) . It is seen that both red and blue tra- jectories approach the discontinuous periodic solution of (5.69), as time increases. So, the discontinuous cycle is orbitally stable trajectory. Moreover, the green one is a continuous periodic trajectory of (5.69) with initial value (0 , 0 . 05) and it is orbitally asymptotically stable. To sum up, there exists two periodic solutions of (5.69) for the parameter µ = − 0 . 2 , one is continuous, the other one is discontinuous and both solutions are orbitally asymptotically stable. In Fig. 10, the red arcs are the orbit of the system w ith initial value (0 , 0 . 1) and the blue arcs are the trajectory of it with initial value (0 , 0 . 4) . Both trajecto ries approach to the discontinuous cycle of system (5.69), as time increases. Thus, Fig. 10 illustrates the existence of the orbitally stable discontinuous periodic solution if µ = 0 . 2 . In literature, the dynamics in the neighborhood of the grazing points [7]-[10], [13], [18], [19], [36]-[39] is generally analyzed through maps of the Poincar ´ e type. The main analysis is conducted on complex 6 Conclusion Figure 9: The blue, red and green arcs constitute the t rajectories of system (5.69) with µ = − 0 . 2 . The first two approach as time increases to the discontinuou s limit cycle and the third one is the continuous limit cycle itself. Figure 10: The red and blue arcs constitute the traje ctories of the system (5.69) with µ = 0 . 2 . Both orbits approach to the discontinuous limit cycle, as tim e increases. 40 −0.5 0 0.5 1 1.5 2 2.5 −1.5 −1 −0.5 0 0.5 1 1.5 x$_{1}$ (t) x 2 (t) −0.5 0 0.5 1 1.5 2 2.5 −1.5 −1 −0.5 0 0.5 1 1.5