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## 4.3 Control of extended chaos 

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The source of the chaotic motions in system (4.11) is the logistic map A$_{1}$. Therefore, to control the chaos of the entire system, one has to stabilize an unstable periodic solution of the logistic map. The OGY control method [67] is one of the possible ways to do this. We proceed by briefly explaining the method. 

Suppose that the parameter µ in the logistic map A$_{1}$ is allowed to vary in the range [3 . 8 − ϵ, 3 . 8 + ϵ $_{]}$, where ϵ is a given small number. That is, it is not possible (say, it is prohibitively costly or practically infeasible) to simply shift the value of µ to a level that generates non-chaotic dynamics. Let us consider an arbitrary solution { κ$_{j}$ } , κ$_{0}$ ∈ [0 , 1] , of the map and denote by κ ( q $^{)}$, q = 1 , 2 , . . . , p, the target unstable p − periodic orbit to be stabilized. In the OGY control method [79], at each iteration step j after the control mechanism is switched on, we consider the logistic map with the parameter value µ = ¯ µ$_{j}$, where 

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provided that the number on the right-hand side of the formula (4 . 14) belongs to the interval [3 . 8 − 

