consideration of infinitely many almost periodic motions instead of periodic ones provides dynamics with a higher complexity . Therefore, our results may be useful for neural networks to obtain a memory with a larger capacity than that with periodic motions. The extension of chaos through unidirectional couplings has been considered in the theory of syn- chronization [54]-[62]. In our study, we do not consider the chaos synchronization problem, but we say that chaos with infinitely many almost periodic motions is generated. The asymptotic proximity of the solutions underlies the presence of synchronization. However, we do not take into account the solutions from the asymptotic point of view. Furthermore, in the synchronization of chaotic systems, one of the assumptions is that the response system is chaotic in the absence of the driving. On the contrary, in our case, the unperturbed system (1.2) possesses an asymptotically stable almost periodic solution, and therefore, it is non-chaotic. The remaining parts of the paper is organized as follows. In Section 2, we investigate the bounded solutions of (1.1) and their attractiveness property. Section 3 is devoted for chaos through a cascade of almost periodic solutions. In Section 4, we describe the Li-Yorke chaos with infinitely many almost periodic motions and deal with the theoretical results concerned with its appearance in system (1.1). An example is provided in Section 5 by means of unidirectionally coupled Duffing oscillators. In Section 6, the control of the extended chaos as well as the stabilization of tori embedded in the chaotic attractor of the coupled Duffing oscillators are numerically demonstrated. Finally, some concluding remarks are given in Section 7. In the remaining parts of the paper, we will make use of the usual Euclidean norm for vectors and the norm induced by the Euclidean norm for square matrices. Since the matrix A in system (1.1) has eigenvalues all with negative real parts, one can verify that there exist positive numbers N and ω such that ∥ e At ∥ ≤ Ne − ωt for all t ≥ 0 . The following conditions are required. 2 Preliminaries (C1) There exists a positive number L$_{1}$ < ω N such that ‖ G ( t, y$_{1}$ ) − G ( t, y$_{2}$ ) ‖ ≤ L$_{1}$ ‖ y$_{1}$ − y$_{2}$ ‖ for all t ∈ R , y$_{1}$, y$_{2}$ ∈ R $^{n}$; (C2) There exists a positive number M$_{G}$ such that sup t ∈ R , y ∈ R n ‖ G ( t, y ) ‖ ≤ M$_{G}$. Utilizing the theory of quasilinear equations [63], it can be verified under the conditions ( C 1) and ( C 2) that for any given bounded function x ( t ) , there exists a unique bounded on R solution φ$_{x}$$_{(}$$_{t}$$_{)}$ ( t ) of 4