Dynamical braces and dynamical Yang–Baxter maps

Discrete Dynamical Systems: Maps

Many physical systems displaying chaotic behavior are accurately described by mathematical models derived from well-understood physical principles. For example, the fundamental equations of fluid dynamics, namely the Navier–Stokes equations, are obtained from elementary mechanical and thermodynamical considerations. The simplest laser models are built from Maxwell’s laws of electromagnetism and...

K-Dynamical Self Organizing Maps

Neural maps are a very popular class of unsupervised neural networks that project high-dimensional data of the input space onto a neuron position in a low-dimensional output space grid. It is desirable that the projection effectively preserves the structure of the data. In this paper we present a hybrid model called K-Dynamical Self Organizing Maps (KDSOM ) consisting of K Self Organizing Maps ...

Continuous iteration of dynamical maps

Dynamical System and Semi-Hereditarily Hypercyclic Property

In this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the Hypercyclicity Criterion. We characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional Banach space .

PROJECTED DYNAMICAL SYSTEMS AND OPTIMIZATION PROBLEMS

We establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. A corresponding novel neural network model, which is globally convergent and stable in the sense of Lyapunov, is proposed. Both theoretical and numerical approaches are considered. Numerical simulations for three constrained nonlinear optimization problems a...