same is true for the control results discussed in the paper. If one considers an element of the chaotic set as the chaotic function, then we may consider our results through input-output mechanisms where input and output are of the same nature, that is, they are chaotic functions. The paper [7], where we discuss an extension mechanism of chaos, is about the replication of specific types of chaos, such as Devaney, Li-Yorke chaos and chaos obtained through period-doubling cascade. In this process, we consider the generator-replicator systems such that the generator is considered as a system of the form where F : R × R m → R m is a continuous function in all its arguments and the replicator is assumed to have the form where$_{H}$ : R m → R n is a continuous function in all its arguments and Λ is the n × n real valued hyperbolic matrix. The rigorous results of the extension mechanism emphasize that system (1 . 2) is chaotic in the same way as system (1 . 1) . Replication of chaos through intermittency is also shown through simulations in paper [7], where one can find new definitions for chaotic sets of functions, and precise descriptions for the ingredients of Devaney and Li-Yorke chaos in continuous-time dynamics, which are used as tools for the extension procedure. In the case that the matrix Λ represented in system (1.2) is hyperbolic, we have not been able to find a way to insert a term nonlinear in y in the system to preserve the results of paper [7] and, instead, we were forced to handle system (1 . 2) with H ( x, y ) ≡ H ( x ) to achieve success in the theoretical results [6]. In other words, we could not achieve the extension of Devaney and/or Li-Yorke chaos when nonlinearity with respect to y is included in the system and the eigenvalues of the matrix Λ are allowed to possess positive real parts as well as negative real parts. However, in the present paper, the chaos extension problem in the sense of Li-Yorke is considered for a hyperbolic matrix Λ and with the nonlinear term of the initially non-perturbed system is also considered for a theoretically supported chaotification process, and this is the main difference compared to [6, 7]. Traditionally, analysis of nonlinear dynamical systems has been restricted to smooth problems, that is, smooth differential equations. Besides stability analysis of fixed points or periodic orbits, another fascinating phenomenon has been found: the existence of chaotic orbits. The presence of these orbits has the consequence that the motions of the system depend sensitively on initial conditions and the asymptotic behavior of orbits in the future is unpredictable. Such a chaotic behavior of solutions can 2 x ′ = F ( t, x ) , (1.1) y ′ = Λ y + H ( x, y ) , (1.2)