We study the existence, structure and stability of periodic solutions of nonlinear systems referred to in the title.

We study dynamical properties of a complex equation with spatially-distributed parameters. Families of special parabolic equations that de¯ne the behavior of initial problem solutions were built.

A morphism of the reduced Gieseker - Maruyama moduli functor (of semistable coherent torsion-free sheaves) on the surface to the reduced moduli functor of admissible semistable pairs with the same Hilbert polynomial, is constructed. It is shown that main components of reduced moduli scheme for semistable admissible pairs ((eS; eL); eE) are isomorphic to main components of the reduced Gieseker - Maruyama moduli scheme.

We consider symmetric Bernoulli measures and new weak metrics and obtain a closed-form expression of the entropy estimator bias.

The problem of the existence of the solutions of polynomial Volterra integral equations of the first kind of the second degree is considered. An algorithm of the numerical solution of one class of Volterra nonlinear systems of the first kind is developed. Numerical results for test examples are presented.

A perspective model of the neuron cell | the generalized neural element (GNE) is studied in this article. This model has the universal character. It combines properties of the neuron-oscillator and the neuron-detector. The problem of adaptation of the generalized neural element is formulated and solved.

In this paper we define a generalized solution of an initial boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We have proved the existence theorem for a generalized solution, its uniqueness, the correctness of the problem. An analytical formula for the solution is found. Such a system of differential equations arises in the study of discrete-continuum mechanical systems.