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$_{5}$. Figure 1: The connection topology of the systems A$_{1}$ − A$_{5}$. 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 10 ν$_{1}$ ( t, θ ) =     0 . 019 , if θ$_{2}$$_{j}$ < t ≤ θ$_{2}$$_{j}$$_{+1}$, 0 . 002 , if θ$_{2}$$_{j}$ − 1 < t ≤ θ$_{2}$$_{j}$, (4.12) κ$_{j}$$_{+1}$ = µκ$_{j}$ (1 − κ$_{j}$ ) , } A$_{1}$ y ′ 1 = (1 / 8) y$_{1}$ − (5 / 16) k$_{1}$ − a$_{1}$y 3 1 − 3 √ a$_{1}$ 2 y 2 1 + ν$_{1}$ ( t, θ ) , k ′ 1 = (1 / 4) y$_{1}$ − (3 / 8) k$_{1}$ − a$_{1}$y 3 1 − 3 √ a$_{1}$ 2 y 2 $_{$_{1}$,}$   $^{A$_{2}$}$ y ′ 2 = (1 / 3) y$_{2}$ − k$_{2}$ − a$_{2}$y 3 2 − √$_{6}$$_{a}$$_{2}$ 2 y 2 + 0 . 6 y$_{1}$ ( t ) + ν$_{2}$ ( t, ζ ) , k ′ 2 = (1 / 2) y$_{2}$ − (5 / 4) k$_{2}$ − a$_{2}$y 3 2 − √$_{6}$$_{a}$$_{2}$ 2 y 2 $_{2}$,    $^{A$_{3}$}$ S ′ = 0 . 23 Y + 0 . 1 S (1 − Y $^{2}$) , Y ′ = 0 . 5( S + F ) + 2( y$_{1}$ ( t ) + 0 . 5) , F ′ = 0 . 19 S − 0 . 25 Y,     $^{A$_{4}$}$ y ′ 3 = (3 / 5) y$_{3}$ − (4 / 5) k$_{3}$ − a$_{3}$y 3 − 3 √ a$_{3}$ √$_{10}$ y 2 3 + 0 . 01 Y ( t ) , k ′ 3 = (7 / 10) y$_{3}$ − (9 / 10) k$_{3}$ − a$_{3}$y 3 − 3 √ a$_{3}$ √$_{10}$ y 2 $_{3}$,    (4.11) 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}$$_{j}$ for each j. ν$_{2}$ ( t, ζ ) =     0 . 0006 , if ζ$_{2}$$_{j}$ < t ≤ ζ$_{2}$$_{j}$$_{+1}$, 0 . 0017 , if ζ$_{2}$$_{j}$ − 1 < t ≤ ζ$_{2}$$_{j}$, . (4.13)