In the present paper, we consider the class of dynamical systems induced by mappings of the Euclidean space R~N of the form φ(v) = B(v+Φ(v))t, v ∈ R~N, (0) where B is a nonsingular matrix and the nonlinearity Φ is determined by the choice of a scalar function f(x), x ∈ R (for a rigorous definition, see Section 1).
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