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Chaotification for linear delay difference equations

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Figure

Figure 1 2-D computer simulation result shows simple dynamical behaviors of the uncontrolledsystem (4) in the (u1,u2) space for k = 1.
Figure 2 2-D computer simulation result shows complex dynamical behaviors of the controlledsystem (5) in the (u1,u2) space for k = 1, β = 10, γ1 = 2π + arcsin 120 , γ2 = arcsin 140 .
Figure 4 3-D computer simulation result shows complex dynamical behaviors of the controlledsystem (5) in the (u1,u2,u3) space for k = 2, β = 10, γ1 = 2π + arcsin 120 , γ2 = arcsin 140 , γ3 = arcsin 160

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