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Scientific program of Shilnikov WorkShop 2021

Date: 16.12.2021



9-45 - 10-00

                                            Opening Conference

Morning session: chairnam Gonchenko S. 



Title of the talk


Belykh V.N. 

Two-dimensional auxiliary systems method


Treshchev D.V.

On isochronous systems

11-30 – 12-15

Ilyashenko Yu.S.

Glocal bifurcations in generic two-parameter families of vector fields on a sphere: a review of problems 

12-15 – 12-45

Morozov A.D., Morozov K.E.

On degenerate resonances and synchronization
of quasiperiodic oscillations

Session dedicated to the 75th anniversary of V.Z. Grines

13-00 – 13-30

Zhuzhoma E.V.

On codimension one basic sets of A-flows

13-30 – 14-00

Pochinka O.V.

On the scientific achievements of the Nizhny Novgorod school of topological methods of dynamics


Evening session: chairman Lerman L. 

14-30 – 15-00

Kasatkin D.V., Nekorkin V.I.

Synchronous patterns in Kuramoto networks with adaptive couplings

15-00 - 15-30

M.A.Garasev, A.A.Nechaev, A.N.Stepanov, V.V.Kocharovsky, Vl.V.Kocharovsky   

Multi-scale magnetic field structures in an expanding elongated plasma cloud with hot electrons subject to an external magnetic field

15-30 - 16-00

Kashchenko S.A.

Infinite Turing Bifurcations in Chains of Van der Pol Systems

16-00- 16-30

А.С. Дмитриев, В.В. Ицков, М. М. Петросян, А.И. Рыжов 

 Радиосвязь на хаотических сигналах в дециметровом диапазоне частот

Sectional talks


Bifurcations and strange            attractors chairman Gonchenko A.S. 

Theory of dynamical systems chairman Morozov K.E. 

Applications of dynamical    systems chairman Rassadin A.E. 

16-40- 17-10

Stankevich N.V., Kuznetsov A.P. “Quasi-periodic bifurcations and complex dynamics in two coupled modified Anishchenko-Astakhov generators”

Efremova L.S. “Periodic trajectories of geometrically integrable maps in the plane

Kulikov A. N., Kulikov D. A. “Invariant manifolds of two versions of the weakly dissipative complex Ginzburg-Landau equation

17-10 - 17-30

A.M. Arefev, E.A. Grines, G.V.Osipov “Heteroclinic cycles and chaos in system of four identical phase oscillators with biharmonic coupling”

Trifonov K.N. “Partially Hyperbolic Symplectic Automorphisms of 4-Torus”

Rassadin A.E.”Remark on the dynamical system in the space of double-sided sequences”

17-30 - 17-50

 Emelin A.E, Levanova T.A., Osipov G.V .”Dynamics in a phase model of half-center oscillator with inhibitory couplings”

Baldoma I., Giralt M., Guardia,M. “Beyond all orders breakdown of the homoclinic connection to L3”

Shamanaev P.A. “Periodic solutions of linear inhomogeneous differential equations with two small parameters”

17-50 - 18-10

Slepukhina E. S. “Transitions between tonic spiking and bursting in the stochastic Hindmarsh-Rose neuron model with the Lukyanov-Shilnikov bifurcation”

Lubchenko D.O., Savin A.V. “The Maxwell's billiard demon effect in simplified Tennison-Lichtenberg-Lieberman system with oscillating boundaries”

Loginov D.O.“On the influence of boundary conditions on the dynamic properties of a logistic equation with delay and diffusion”

18-10 - 18-30

Garashchuk I.R.Asynchronous chaos and bifurcations in a model of two coupled Hindmarsh-Rose neurons”

Golokolenov A. V., Savin D. V. “Self-oscillating system with weak dissipation demonstrating the <> in the conservative limit: approximations, evolution of attractors and chaos in the phase space”

Golubenets V.O. “Relaxation solutions in a logistic equation with state-in-the-past-dependent delay”



Date: 17.12.2021



Morning session: chairnam Malkin M.I.



Title of the talk


Grines V.Z. 

Topology of ambient manifolds and chaotic hyperbolic dynamics


Lerman L.M.

Nonautonomous Dynamics: the Uniform Approach

11-20 – 11-50

Alfimov G.L.,  Zezyulin D.A.,               Slobodyanyuk A.O.

Nonlinear modes and pseudo-modes for NLS equation
with complex potential

11-50 – 12-30

Fiedler B.

Real chaos, and complex time

12-30 – 13-00

Vieiro A.

Escape times across a golden Cantorus and the evolution
 of approximant islands

13-00 – 13-40

Gelfreich V. 

Singularly embedded solitons in the fifth order KdV model

13-40 – 14-20

Kuptsov P.

Concept of instant Lyapunov exponents and their application for
numerical analysis of attractors structure

Small break

Evening session: chairman Kazakov A.O.

14-30 – 15-00

Malkin M., Safonov K.

One-dimensional factor maps of stable folliations for Lorenz and Rovella attractors

15-00- 15-30

Ovsyannikov I.I.

Universal bounds in Lorenz-like systems

15-30 - 16-00

Turaev D.

A model of a pseudohyperbolic Shilnikov attractor

16-00 - 16-30

Pikovsky A., Nepomnyashchy A.  

Chaos in coupled heteroclinic cycles and its picewise-linear        description

16-30 – 17.00

Kruglov V.P., Kazakov A.O., Karatetskaya E.Yu.,  Gonchenko S.V.

On new pseudohyperbolic attractor of Lorenz type

17-00 – 17.30

Tali Pinsky

A heteroclinic trefoil for the Lorenz equations.

17-30 – 18.30

Shilnikov A.L.

Leonid Shilnikov and mathematical theory of dynamical chaos






Astrakharchik G.E.

Making stable the shear modulus instability


Barabash N.V., Stasenko S.V.,    Levanova T.A.

 Stable burstings in a STSP model with glia's impact


Belykh V.N., Barabash N.V.,     Belykh I.V.

Non-classical homoclinic bifurcation in a piecewise-smooth Lorenz-type system


Chigarev V., Kazakov A., Pikovsky A.

On the collision of a chaotic attractor with a chaotic repeller leading to the emergency of hyperchaotic orbits


Grechko D.A., Belykh V.N.

Localization of attractors of maps using auxiliary one-dimensional maps


Gonchenko A.S., Samylina E.A.

On discrete homoclinic attractors of three-dimensional maps


Gonchenko M.S.

Reversible perturbations of Henon-like maps.


Gordeeva O.V.

On local maps near nonhyperbolic periodic orbits


Karatetskaya E.Yu.

Multistability and hyperchaos in models of coupled repressilators


Sinelshchikov D.I.

 Integrability criteria for a family of cubic oscillators


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