of this set is considered as a chaotic function. Both a set of functions and a single function can serve as an input (as well as an output), and we will use both types of inputs and outputs in this study. We consider base-systems of two kinds: (i) systems with asymptotically stable equilibria, (ii) systems with limit cycles. In the former case, we will talk about attraction of chaos by equilibria, and in particular, attraction of cyclic chaos by equilibria. If the base-system admits a limit cycle, then we talk about the entrainment by chaos of limit cycles or just about entrainment by chaos [9]. If the limit cycle in a base-system is the result of a Hopf bifurcation [43], we will also talk about the bifurcation of the cyclic chaos. In our previous papers [2, 5, 6, 7, 8] we analyzed the extension of chaos when the base system possesses an asymptotically stable equilibrium. The present paper focuses mostly on the generation of cyclic chaos through unilateral coupling of multiple systems. The main source of chaos in theory are difference and differential equations. For this reason we consider in our manuscript, inputs, which are solutions of some systems of differential or discrete equations equations. These systems will be called generators . 2 Thus, we consider the following system of differential equations, where the function G : [0 , ∞ ) × R m → R m is continuous in all of its arguments. We assume that system (2.3) possesses a chaotic attractor, and we call this system a generator . If x ( t ) is a solution of the system from the chaotic attractor, then we take and use the function I ( t ) in equation (2.2). Here, ϵ is a non-zero real number and the function ψ : R m → R n is continuous. Since we use x ( t ) as a perturbation in the network (2.2), we call it a chaotic solution . The chaotic solutions may be irregular as well as regular (periodic and unstable) [30, 33, 77, 78]. In this study we will utilize also the logistic map [30] as a generator. System (2.3) is called sensitive if there exist positive numbers ϵ$_{0}$ and Δ such that for an arbitrary positive number δ$_{0}$ and for each chaotic solution x ( t ) of (2.3), there exist a chaotic solution x ( t ) of the same system and an interval J ⊂ [0 , ∞ ) , with a length no less than Δ , such that ‖ x (0) − x (0) ‖ < δ$_{0}$ and ‖ x ( t ) − x ( t ) ‖ > ϵ$_{0}$ for all t ∈ J. For a given chaotic solution x ( t ) of (2.3), let us denote by η$_{x}$$_{(}$$_{t}$$_{)}$ ( t, y$_{0}$ ) , y$_{0}$ ∈ R $^{n}$, the solution of (2.2) with η$_{x}$$_{(}$$_{t}$$_{)}$ (0 , y$_{0}$ ) = y$_{0}$. System (2.2) replicates the sensitivity of (2.3) if there exist positive numbers ϵ$_{1}$ $^{2}$In future work, economic time series that have been tested for the presence of deterministic chaos may be considered (see [21, 23, 29, 68, 86].) 6 x ′ = G ( t, x ) , (2.3) I ( t ) = εψ ( x ( t )) ,