dynamic system, and find that similar chaos is inherited by the solutions of the new system. We call this as the input-output mechanism of chaos generation . This approach has been widely applied to differential equations before, but for regular inputs. In the studies [2, 3, 4, 6, 8], the mechanisms for generating chaos in systems with asymptotically stable equilibria are provided. In contrast, in [54, 55, 56, 60] unpredictability in the solutions of differential equations was considered a result of random perturbations with small probability. P.A. Samuelson [76] accepts purely endogenous theory as “self-generating” cycle. Following this opinion we understand chaos as endogenous if it is self-generated by an economic model. One can find detailed analysis of the endogenous chaos in books [58, 74, 88] and paper [15], which are very seminal sources on the subject. The dynamics arise in duopoly models [73], in simple ad hoc macroeconomic models [28, 80]. By applying the Li-Yorke theorem it is shown in [16, 17] that an overlapping generations model of the Gale type could generate endogenous chaotic cycles. Discrete equations have been applied to investigate the presence of chaos in papers [26, 27], where models representing a capital stock with a maximum capital-labor ratio and a Malthusian agrarian economy are investigated. In [25, 27, 71] endogenous chaotic cycles are demonstrated in growth cycle models. The multiplier-accelerator model of Samuelson [76] has been modified for generation of chaotic endogenous cycles and investigated in [18, 36, 66]. Investigations in Kaldor’s type models, which are originated from [44, 18] and finalized in [22], showed that they could generate endogenous chaos. Economists of the first half of the last century already felt a strong need for a theory of irregularities, particularly of irregular business cycles. In his classic book, Samuelson [76] observes that while forced oscillator systems naturally emerge in theoretical investigations of several technical and physical devices and phenomena, economic examples for this special family of functions have only rarely been provided. The main reason for this dearth of evidence may lie in the fact that the necessary periodicity of the dynamic forcing may not be obvious in most economic applications. That is, economic phenomena do not display the kind of regularity that physical phenomena do. Samuelson [76] states that “... in a physical system there are grand conservation laws of nature, which guarantee that the system must fall on the thin line between stability and instability. But there is nothing in the economic world corresponding to these laws ...". In a passage Samuelson [76] suggests that “It is to be stressed that the exogenous impulses which keep the cycle alive need not themselves be even quasi-oscillatory in character." Thus, he was already talking about irregular business cycles that emerge as a result of irregular exogenous shocks . Moreover, he recognized that “most economists are eclectic and prefer a combination of endogenous and exogenous theories." Accordingly, in the present paper we consider economic models that admit endogenous business cycles and are perturbed by exogenous chaotic disturbances. Examples of models possessing limit cycles are Kaldor-Kalecki models and Lienard type equations with relaxation oscillations which are popular in economics. Next, the systems are subject to exogenous chaotic disturbances, sensitive and with infinitely 3