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Suppose that k$_{1}$ is the smallest natural number satisfying Δ ≤ k$_{1}$. In this case, we have for each k ≥ k$_{1}$ that 

Hence, for each n ∈ N , the inequality 

holds, where 

The theorem is proved. □ 

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In the definition of Devaney chaos, periodic motions constitute a dense subset. However, in our case, instead of periodic motions, Poisson stable motions take place in the dynamics. More precisely, we say that the dynamics on the quasi-minimal set of functions on R is chaotic if the dynamics on it is sensitive, transitive and there exists a continuum of Poisson stable trajectories dense in the quasi-minimal set. Nevertheless, in the framework of chaos there may be infinitely many periodic motions. For instance, the symbolic dynamics of bi-infinite sequences possesses both an uncountable set of non-periodic Poisson stable motions as well as infinitely many cycles [1, 15]. 

## 5 An Example 

In this part of the paper, we will present an illustrative example. For that purpose, we will make use of coupled Duffing equations such that the first one is forced with a relay function and the second one is perturbed with the solutions of the former. 

Let us consider the following forced Duffing equation, 

where the forcing term ν ( t, ζ, λ ) is a relay function defined as 

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In (5.10), the sequence ζ = { ζ$_{j}$ }$_{j}$$_{∈}$$_{Z}$ of switching moments is defined through the equation ζ$_{j}$ = j + κ$_{j}$, 

