content_image/321588.jpg content_image/321585.jpg content_image/321584.jpg content_image/321587.jpg
of the connection is presented in Figure 1, and the models are formulated in system (4.11). We will show that the chaos that appears in A$_{1}$ spreads to all the other models. A$_{2}$ serves as a replicator of the chaos of A$_{1}$ and as a generator of chaos in A$_{3}$ and A$_{4}$. Model A$_{4}$ is a replicator of the chaos of A$_{2}$ and a generator of chaos in A$_{5}$. 

The following is a system of five unidirectionally coupled models A$_{1}$ − A$_{5}$. 

<img src='content_image/321588.jpg'>

<img src='content_image/321585.jpg'>

where a$_{1}$, a$_{2}$, a$_{3}$ are constants and the piecewise constant functions ν$_{1}$ ( t, θ ) and ν$_{2}$ ( t, ζ ) are defined as follows: 

and 

The sequence θ = { θ$_{j}$ } , j ∈ Z , of the discontinuity instants of the function (4.12) satisfies the relation θ$_{j}$ = j + κ$_{j}$, where the sequence { κ$_{j}$ } is a solution of the logistic map A$_{1}$ with κ$_{0}$ ∈ [0 , 1] . The sequence ζ = { ζ$_{j}$ } , j ∈ Z , of the discontinuity instants of (4.13) satisfies the relation ζ$_{j}$ $_{= 2}$√$_{2}$$_{j}$ for each j. 

<img src='content_image/321584.jpg'>

<img src='content_image/321587.jpg'>

