The first mathematical definition of chaos was introduced in the paper [2] for discrete-time systems. According to Li and Yorke [2], a continuous map on an interval has points of all periods provided that it has a point of period three, and there exists an uncountable scrambled subset [16] of the interval. The part of the Li-Yorke Theorem concerning periodic motions is a specific version of the Sharkovskii Theorem [17]. The presence of the scrambled set is the feature that distinguishes Li-Yorke chaos from other types [16]. Besides, a possible way for systems to achieve chaos is the period-doubling cascade, which was first observed in quadratic maps by Myrberg [18]-[20]. In this phenomenon, as some experimental parameter of the considered system varies, a motion with a fundamental period changes to a periodic motion with twice the period of the original oscillation, and as the parameter is changed further, the same procedure occurs. The period-doubling bifurcation values of the parameter accumulates at a finite value, after which chaos is observable [3, 21, 22]. The period-doubling onset of chaos exhibits universal behavior [3], and it can be observed in many nonlinear systems, particularly in neural networks [23], ecological models [24], nonlinear circuits [25], and semiconductor lasers [26]. Throughout the paper, R , N and Z will denote the sets of real numbers, natural numbers and integers, respectively. The main object of the present investigation is the dynamics of the following system, where the function G : R × R n → R n is continuous in both of its arguments and it is almost periodic in t uniformly for y ∈ R $^{n}$, the function H : R m → R n is continuous, and all eigenvalues of the constant n × n real valued matrix A have negative real parts. Equation (1.1) is obtained by perturbing the system with the term H ( x ( t )) . The perturbation function x ( t ) will be explained in a detailed form in Section 3 and Section 4. Our purpose is to prove rigorously that if the perturbation is chaotic, then system (1.1) possesses chaos with infinitely many almost periodic motions . We will make use of coupled Duffing oscillators to illustrate the formation of the chaos. Moreover, the controllability of the generated chaos will be demonstrated numerically. In the present study, two different types of chaos formation will be presented. In the first one, solutions of a system of differential equations that possesses a period-doubling cascade will be utilized as the perturbation function x ( t ) in (1.1). Secondly, we will make use of chaotic sets of functions as the source for the perturbation x ( t ) to obtain Li-Yorke chaos with infinitely many almost periodic motions, which are separated from the scrambled set. The main difficulty of indicating almost periodicity in chaos lies in the fact that systems which generate chaos do this with periodical scenario. Being based on special input-output mechanisms, the y ′ = Ay + G ( t, y ) + H ( x ( t )) , (1.1) u ′ = Au + G ( t, u ) (1.2) 2