Boolean Dynamical Systems (BDSs) are networks described by variables. A new representation of BDSs is presented in this article using modal non-monotonic logic (\({\mathcal {H}}\)). This approach allows Networks to be represented a set formulas and therefore can used describe learn their properties. The study BDS focuses particular on the search stable configurations, limit cycles unstable cycl...

Abstmct We focus on the training scheme for the neural networks t o learn in the regions of unstable equilibrium states and the identification and the control using these networks. These can be achieved by introducing a supervisory controller during the learning period of the neural networks. The supervisory controller is derigned based on Lyapunov theory and it guarantees the bonndednese of th...

Existence and uniqueness theorems for unstable manifolds are well-known. Here we prove certain refinements. Let f : (C, 0) → C be a germ of an analytic diffeomorphism, whose derivative Df(0) has eigenvalues λ1, . . . , λn such that |λ1| ≥ · · · ≥ |λk| > |λk+1| ≥ · · · ≥ |λn|, with |λk| > 1. Then there is a unique k-dimensional invariant submanifold whose tangent space is spanned by the generali...

We construct complex networks from pseudoperiodic time series, with each cycle represented by a single node in the network. We investigate the statistical properties of these networks for various time series and find that time series with different dynamics exhibit distinct topological structures. Specifically, noisy periodic signals correspond to random networks, and chaotic time series genera...