140 citations · 394 across the 23 of their papers we have counts for
23 papers
An improved approach for estimating the dimension of inertial manifolds in chaotic distributed dynamical systems via analysis of angles between tangent subspaces
Pavel V. Kuptsov
While a previously proposed method for estimating inertial manifold dimension, based on explicitly computing angles between pairs of covariant Lyapunov vectors (CLVs), employs effi…
Reconstruction of neuromorphic dynamics from a single scalar time series using variational autoencoder and neural network map
Pavel V. Kuptsov, Nataliya V. Stankevich
This paper examines the reconstruction of a family of dynamical systems with neuromorphic behavior using a single scalar time series. A model of a physiological neuron based on the…
Discovering dynamical features of Hodgkin-Huxley-type model of physiological neuron using artificial neural network
Pavel V. Kuptsov, Nataliya V. Stankevich, Elmira R. Bagautdinova
We consider Hodgkin-Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the mode…
Analysis of three non-identical Josephson junctions by the method of Lyapunov exponents charts
Alexander P. Kuznetsov, Igor R. Sataev, Pavel V. Kuptsov +1
A system of three non-identical Josephson junctions connected via an RLC circuit is considered. The method of Lyapunov exponents charts is used, which makes it possible to identify…
Artificial neural network as a universal model of nonlinear dynamical systems
Pavel V. Kuptsov, Anna V. Kuptsova, Nataliya V. Stankevich
We suggest a universal map capable to recover a behavior of a wide range of dynamical systems given by ODEs. The map is built as an artificial neural network whose weights encode a…
Estimating of the inertial manifold dimension for a chaotic attractor of complex Ginzburg-Landau equation using a neural network
Pavel V. Kuptsov, Anna V. Kuptsova
Dimension of an inertial manifold for a chaotic attractor of spatially distributed system is estimated using autoencoder neural network. The inertial manifold is a low dimensional…