where the function F : R × R m → R m is continuous in all its arguments and f : R × R n → R n is continuous, C 2 function in x and satisfy the following conditions: To extend chaos generated by equation (2.3), we perturb system (2.4) through the solutions of (2.3) to achieve the system where h : R m → R n is a continuous function. The system (2.3) has infinitely many periodic solutions as well as the system (2.4) around a homoclinic orbit q ( t $_{)}$. If the fundamental periods of the systems (2.3) and (2.4) are commensurable, that is the quotient of the fundamental periods are rational, then the system (2.5) has periodic solutions. Otherwise, if the fundamental periods of the systems (2.3) and (2.4) are incommensurable, the system (2.5) has quasi-periodic or more general almost periodic solutions. Thus, in this study Li-Yorke chaos is generated with infinitely many almost periodic motions in basis instead of periodic motions. Throughout the paper, we will make use of the usual Euclidean norm for vectors and the norm induced by the Euclidean norm for matrices [30]. The following conditions are required: for all x$_{1}$, x$_{2}$ ∈ R $^{m}$, and for all u$_{1}$, u$_{2}$ ∈ R $^{n}$, t ∈ R . It is worth noting that the results of our study are also true even if we replace the non-autonomous system (2.3) by the autonomous equation where the function F : R m → R m is continuous with the condition which is a counterpart of ( C $_{3)}$. 4 x ′ = F ( x ) , (2.6) ‖ f ( u$_{1}$, t ) − f ( u$_{2}$, t )) ‖ ≤ L$_{3}$ ‖ u$_{1}$ − u$_{2}$ ‖ L$_{1}$ ‖ x$_{1}$ − x$_{2}$ ‖ ≤ ‖ h ( x$_{1}$ ) − h ( x$_{2}$ ) ‖ ≤ L$_{2}$ ‖ x$_{1}$ − x$_{2}$ ‖ u ′ = f ( u, t ) + h ( x ) , (2.5) ($_{C1}$) f is $_{1}$-periodic in t ; ($_{C2}$) The system (2.4) has a hyperbolic periodic solution p ( t ) with a homoclinic solution q ( t ) such that the variational equation v ′ = D$_{u}$f ( q ( t ) , t ) v has the only zero solution bounded on R . (C3) There exists a positive number H$_{0}$ such that sup x ∈ R $^{m}$,t ∈ R ‖ F ( x, t ) ‖ ≤ H$_{0}$ ; (C4) There exist positive numbers L$_{1}$, L$_{2}$ and L$_{3}$ such that