written as where D =    − 2 0 0 0 − 3 0 0 0 − 1   $^{,}$ and System (6.13) admits an unpredictable solution ψ ( t ) in accordance with Theorem 5.1. Therefore, Corollary 5.1 implies that ψ ( t ) = P ψ ( t ) is an unpredictable solution of (6.11). To demonstrate the chaotic behavior, we depict in Figure 2 the x$_{2}$ − coordinate of the solution of (6.11) corresponding to the initial data x$_{1}$ ( ζ$_{0}$ ) = 0 . 17 , x$_{2}$ ( ζ$_{0}$ ) = 0 . 51 , x$_{3}$ ( ζ$_{0}$ ) = 0 . 48 , ζ$_{0}$ = 0 . 4 . The coefficient µ = 3 . 86 and the initial value ζ$_{0}$ = 0 . 4 are considered for shadowing in [22]. The chaotic behavior is also valid in the remaining coordinates, which are not just pictured here. Moreover, Figure 3 shows the 3 − dimensional chaotic trajectory of the same solution. It is worth noting that the chaotic solutions of (6.11) take place inside the compact region Figures 2 and 3 support the results of Theorem 5.1 and Corollary 5.1 such that the represented solution behaves chaotically. Now, we will demonstrate the extension of unpredictable solutions and Poincaré chaos. For that purpose, we consider the system 13 z $^{′}$( t ) = Bz ( t ) + f ( z ( t )) + h ( ψ ( t )) , (6.15) H = { ( x$_{1}$, x$_{2}$, x$_{3}$ ) ∈ R 3 | − 1 ≤ x$_{1}$ ≤ 1 . 1 , 0 . 3 ≤ x$_{2}$ ≤ 1 , − 0 . 4 ≤ x$_{3}$ ≤ 1 . 9 } . (6.14) ν ( t ) =     (0 , 0 , − 1) , if ζ$_{2}$$_{j}$ < t ≤ ζ$_{2}$$_{j}$$_{+1}$, j ∈ $^{Z}$, (1 , 1 , 0) , if ζ$_{2}$$_{j}$ − 1 < t ≤ ζ$_{2}$$_{j}$, j ∈ $^{Z}$. y $^{′}$( t ) = Dy ( t ) + ν ( t ) , (6.13) Figure 2: The x$_{2}$ − coordinate of the chaotic solution of system (6.11). 0 10 20 30 40 50 60 70 80 90 100 0.4 0.6 0.8 t x 2