Inertial manifolds and limit cycles of dynamical systems in Rn

We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in ${\mathbb R}^{n}$ permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincare--Bendixson theory. In the case $n=3$ we implement such a scenario for a model of a satellite rotation around a celestial body of small mass and for a biochemical model

Substantiation of the minimum size of the trial area when estimating the yield of chaga in birch plants of Perm Region

The article discusses the results of mantle tinder (Inonotus obliquus) productivity studies in the birch plantings of Kizelovsky and Kungursky forestry in Perm Region. The aim of the study was to establish the optimal size of the trial plot laid in the plantation and providing representative data on the fungus production. Distances between infected trees exceed 100 meters. The minimum trial area should be 3 hectares. In the studied territories, chaga production was 0.5–2.7 kg / ha in fresh weight

Inertial manifolds and limit cycles of dynamical systems in Rn

We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in Rn permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincaré–Bendixson theory. In the case n = 3 we implement such a scenario for a model of a satellite rotation around a celestial body of small mass and for a biochemical model