24 citations · 24 across the 5 of their papers we have counts for
5 papers
Twisted homoclinic orbits in Lorenz and Chen systems: rigorous proofs from universal normal form
Vladimir N. Belykh, Nikita V. Barabash, Anastasia E. Suroegina
The properties common to the Lorenz and Chen attractors, as well as their fundamental differences, have been studied for many years in a vast number of works and remain a topic far…
Analytically tractable reconstruction of singular hyperbolic and quasi-strange attractors of Lorenz-type systems
Nikita V. Barabash, Daria A. Bakalina, Vladimir N. Belykh
We consider a certain three-dimensional piecewise linear system of Lorenz type in the cases of positive and negative saddle value, which is the sum of two eigenvalues of the saddle…
Existence of an attractor and Horseshoe in multidimensional Hénon map
Dina A. Grechko, Vladimir N. Belykh, Nikita V. Barabash
In this paper using approach of 1-D auxiliary maps we prove the existence of trapping domains containing attractors of the multidimensional Henon-like maps. For both of quadratic a…
Invariant cones for strange attractors of Lozi, Hénon and Belykh type maps
Dina Grechko, Vladimir Belykh, Nikita Barabash
We consider strange attractors of two dimensional generalized map with one nonlinearity such that Lozi, Hénon and Belykh maps are particular cases of it. We describe technique of i…
Rhythmogenesis in the mean field model of the neuron-glial network
Nikita Barabash, Tatiana Levanova, Sergey Stasenko
Despite the fact that the phenomenon of bursting activity is important for functioning of living neural networks, the mechanisms of its origin are still not clear. In this paper, w…