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systems (5.12) and (5.16) to set up the system 

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System (5.17) is in the form of (1.6) with h ( x$_{1}$, x$_{2}$ ) =    0 . 7 x 2 1 − 1 . 2 x$_{1}$ arctan( x$_{2}$ )    . It can be numerically verified that the bounded solutions of (5.17) lie inside t he compact region 

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Therefore, the conditions ( C 1) and ( C 2) are valid f or (5.17) with M$_{f}$ = 1 . 50729 and L$_{f}$ = 0 . 0243 . Moreover, the function h ( x$_{1}$, x$_{2}$ ) clearly satisfies the conditions ( C 4) and ( C 5) on the compact region Λ defined by (5.13). The chaos of system (5.16) is pers istent under the applied perturbation such that system (5.17) possesses Li-Yorke chaos with infinitely many almost periodic motions in basis according to Theorem 4.1. 

Using the solution ( x$_{1}$ ( t ) , x$_{2}$ ( t )) of (5.12) whose first coordinate is represented in Figure 1 in the perturbation, we depict in Figure 3 the y$_{1}$ − coordin ate of the solution of (5.17) corresponding to the initial data ζ$_{0}$ = 0 . 56 , y$_{1}$ ( t$_{0}$ ) = 0 . 43 , y$_{2}$ ( t$_{0}$ ) = 0 . 04 , w here t$_{0}$ = 0 . 56 . Furthermore, Figure 4 shows the trajectory of the same solution on the y$_{1}$ − y$_{2}$ plan e . Both of Figures 3 and 4 support the result of Theorem 4.1 such that Li-Yorke chaos is permanent in the dynamics of (5.16) even if the perturbation h ( x$_{1}$, x$_{2}$ ) is applied. 

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