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Modeling and Analysis of Information Systems

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Vol 20, No 1 (2013)

Articles

5-17 1014
Abstract

Given a bisingular parabolic problem for a system of linear parabolic equations, we construct an asymptotics for the solution of any order with respect to a small parameter, without using the joining procedure for asymptotic expansions.

18-29 967
Abstract
We study a model of single-mode semiconductor laser with the optical feedback. This model bases on DDE (Lang–Kobayashi model). With the help of local analysis methods we built a continuous set of quasinormal forms in the neighbourhood of critical values. The ability of coexistence of a large number of steady oscillating states is discussed.
30-51 1021
Abstract

The phenomenon of multimode diffusion chaos is considered. For a number of examples it is shown that the Lyapunov dimension of the attractor of a distributed dynamical system increases as the diffusion coefficient tends to 0.

52-98 946
Abstract

A new asymptotic method for investigating complex relaxation oscillations of a system with delay was offered. Applying it, we can reduce the problem of predator-prey system dynamics to problem of one-dimensional maps analysis. Some conclusions of biological nature based on the asymptotic analysis were made.

 

99-106 952
Abstract

The behavior of a distributed kinetic system, which is in homogeneous equilibrium within a flat circular reactor, under circular domain deformation is studied. We show that the deformation of domain may lead to appearance of stable spatially inhomogeneous oscillatory solutions, including chaotic oscillations (strange attractors), in the neighborhood of homogeneous equilibrium. We also speak about mechanisms of initiation of chaotic attractors and calculate Lyapunov exponents and Lyapunov dimension for these regimes. We call this mechanism of appearance of spatially inhomogeneous nonlinear oscillations in distributed kinetic system the domain effect.

107-115 852
Abstract
A new class of metrics on a space of right-sided infinite sequences drawn from a binary alphabet was introduced.
116-123 860
Abstract
Let π be a set of primes. For Baumslag — Solitar groups the necessary and sufficient condition to be virtual residuality by finite π–groups is obtained.
124-132 839
Abstract

Let G be a free product of residually finite virtually soluble groups A and B of finite rank with an amalgamated subgroup H, H 6= A and H 6= B. And let H contains a subgroup W of finite index which is normal in both A and B. We prove that the group G is residually finite if and only if the subgroup H is finitely separable in A and B. Also we prove that if all subgroups of A and B are finitely separable in A and B, respectively, all finitely generated subgroups of G are finitely separable in G.

133-137 849
Abstract

Let K be a root class of groups. It is proved that a free product of any family of residually K groups with one amalgamated subgroup, which is a retract in all free factors, is residually K. The sufficient condition for a generalized free product of two groups to be residually K is also obtained, provided that the amalgamated subgroup is normal in one of the free factors and is a retract in another.

138-159 884
Abstract
A carpenter’s rule problem is considered for the case of a self-intersecting planar polygon with additional restriction: the index (turning number) of the polygon should be preserved during deformation. We present a solution for equilateral polygons and state a problem for general ones.


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ISSN 1818-1015 (Print)
ISSN 2313-5417 (Online)