points, they are ∂ Γ = { (0 , 0) , (exp(0 . 00025 π ) , 0) , (exp(0 . 00025 π ) , y$_{2}$ ( θ$_{1}$, 0 , (0 , ¯ y$_{2}$ ))) , (0 , y$_{2}$ ( θ$_{2}$, 0 , − R$_{1}$y$_{2}$ ( θ$_{1}$, 0 , (0 , ¯ y$_{2}$ ))) } . In the following part of the example, we will show that two of them, y ∗ = ( y ∗ $_{1}$, y ∗ $_{2}$) = (exp(0 . 00025 π ) , 0) and the origin, (0 , 0) are grazing points. Moreover, it can be easily validated that other two points are of β − type. Issuing from system (3.14), the curve of discontinuity ˜ Γ consists of two components ˜ Γ$_{1}$ and ˜ Γ$_{2}$ . The components are the following sets and One can verify that the function is a discontinuous periodic solution of (3.14) with period ω = π, whose discontinuity points (0 , 1) and (0 , − exp(0 . 0005 π )) belong to ˜ Γ and Γ , respectively. The expression Ψ( t ) =    $^{exp(0}$$^{.}$$^{0005}$$^{t}$$^{)}$ ( sin( t ) , cos( t ) , if t ∈ [0 , π ) , (0 , 1) , if t = π, (3.15) ˜ Γ$_{2}$ = { ( y$_{1}$, y$_{2}$ ) | y$_{1}$ = 0 , 0 ≤ − R$_{2}$y$_{2}$ ( θ$_{2}$, 0 , Q$_{2}$ ) } . ˜ Γ$_{1}$ = { ( y$_{1}$, y$_{2}$ ) | y$_{1}$ = exp(0 . 00025 π ) , − R$_{1}$y$_{2}$ ( θ$_{1}$, 0 , (0 , ¯ y$_{2}$ )) 2 ≤ y$_{2}$ ≤ 0 } 〈∇ Φ((exp(0 . 00025 π ) , 0)) , f ((exp(0 . 00025 π ) , 0)) 〉 = 〈 (1 , 0) , (0 , − exp( − 0 . 00025 π )) 〉 = 0 verifies that y ∗ is a ( γ ) − type point, i.e. a grazing point of the solution Ψ( t ) . It is easily seen that the grazing is axial. Now, we can assert that the periodic solution (3.15) is a grazing solution in the sense of Definition 2.5. Its simulation is depicted in Figure 2. Figure 2: The grazing orbit of system (3.14). Since the complement of G is invariant in both directions and consists of continuous trajectories of −0.2 0 0.2 0.4 0.6 0.8 1 1.2 −1.5 −1 −0.5 0 0.5 1 1.5 z$_{1}$(t) z 2 (t) 14