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orbitally stable cycle - are introduced. These models are chaotically perturbed in the following section to obtain the main economic dynamics of the paper. More precisely, Section 4 considers a constellation of five economic models connected unilaterally. The extension of chaos near an equilibrium attractor, the entrainment by chaos of limit business cycles, the bifurcation of a chaotic cycle, and the attraction of a chaotic cycle are the scenarios of the appearance of chaos, and in some cases of chaotic business cycles, in economic models that we demonstrate. The effects of applying OGY control [67] to the models will also be presented. Section 5 provides simulation results for the entrainment by chaos of limit cycles of economic models with time delay. We compare in detail our method of chaos generation with that based on the synchronization of chaos [51, 70, 75] in Section 6. In particular, we argue that chaotic business cycles in the paper cannot be obtained by the synchronization of chaotic systems. In Section 7 we discuss our results from the point of view of self-organization, and particularly synergetics of Haken [42]. We summarize the obtained results in the Conclusion. 

## 2 The Input-Output Mechanism and Its Applications 

To explain the input-output mechanism of chaos generation, let us introduce systems, which we call the base-system, the replicator and the generator . They are intensively used in the manuscript. Consider the following system of differential equations, 

<img src='content_image/312173.jpg'>

where B : R n → R n is a continuously differentiable function. The system (2.1) is called the base-system . 

Next, we subdue the base-system to a perturbation, I ( t ) , which will be called an input and obtain the following system, 

which will be called as the replicator . 

<img src='content_image/312174.jpg'>

Suppose that the input I ( t ) admits a certain property, say, it is a bounded function. Assume that there exists a unique solution, y ( t ) , of the replicator system (2.2), with the same property. This solution is called an output . The process of obtaining the solution y ( t ) by applying the perturbation I ( t ) to the base-system (2.1) is called the input-output mechanism . It is known that for certain base-systems, if the input is a periodic, almost periodic, bounded function, then there exists an output that is also a periodic, almost periodic, bounded function. In our paper, we consider inputs of a different nature: chaotic functions and set of cyclic chaotic functions. The motions that are in the chaotic attractor of the Lorenz system [57], considered altogether, give us an example of a chaotic set of functions. Each element 

