differential equations

Adjoint State Method, Backpropagation and Neural ODEs
You probably heard about Neural ODEs, a neural network architecture based on ordinary differential equations. To train this kind of models, a mysterious trick called the adjoint state method is used. How does it work, why do we need it, and how it is related to backpropagation?
Aug 5, 2022 44 min read
Ordinary differential equations
Introductory textbook with focus on important geometrical and dynamical phenomena like conservation laws, stability and bifurcations.
Oct 27, 2021
Read textbook (in Russian)
Ordinary differential equations
Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene
We study tunneling of charge carriers in single- and bilayer graphene. We propose an explanation for nonzero “magic angles” with 100% …
V. Kleptsyn, A. Okunev, I. Schurov, D. Zubov, M. I. Katsnelson
Cite DOI arXiv
On the adjacency quantization in an equation modeling the Josephson effect
We study a two-parameter family of nonautonomous ordinary differential equations on the 2-torus. This family models the Josephson …
A. A. Glutsyuk, V. A. Kleptsyn, D. A. Filimonov, I. V. Schurov
Cite DOI arXiv
Josephson Effect and Fast-Slow Systems
In order to model the processes taking place in systems with Josephson contacts, a differential equation on a torus with three …
O. V. Romaskevich, V. A. Kleptsyn, I. V. Schurov
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Cyclicity of elementary polycycles with fixed number of singular points in generic k-parameter families
An estimate is found for the number of limit cycles arising from polycycles in generic finite-parameter families of differential …
P. I. Kaleda, I. V. Shchurov
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Duck farming on the two-torus: multiple canard cycles in generic slow-fast systems
Generic slow-fast systems with only one (time-scaling) parameter on the two-torus have attracting canard cycles for arbitrary small …
Ilya Schurov
Cite DOI arXiv
Ducks on the torus: existence and uniqueness
We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles …
I. V. Schurov
Cite DOI arXiv