46 citations · 248 across the 17 of their papers we have counts for
19 papers
Attractor-repeller collision and the heterodimensional dynamics
V. Chigarev, A. Kazakov, A. Pikovsky
We study the heterodimensional dynamics in a simple map on a three-dimensional torus. This map consists of a two-dimensional driving Anosov map and a one-dimensional driven Möbius…
On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators
Evgeny A. Grines, Alexey O. Kazakov, Igor R. Sataev
We study chaotic dynamics in a system of four differential equations describing the dynamics of five identical globally coupled phase oscillators with biharmonic coupling. We show…
On Shilnikov attractors of three-dimensional flows and maps
Yuliya Bakhanova, Sergey Gonchenko, Alexander Gonchenko +2
We describe scenarios for the emergence of Shilnikov attractors, i.e. strange attractors containing a saddle-focus with two-dimensional unstable manifold, in the case of three-dime…
Leonid Shilnikov and mathematical theory of dynamical chaos
Alexey Kazakov, Sergey Gonchenko, Dmitry Turaev +1
This Focus Issue Global Bifurcations, Chaos, and Hyperchaos Theory and Applications is dedicated to the 85th anniversary of the great mathematician, one of the founding fathers of…
On 1:3 resonance under reversible perturbations of conservative cubic Hénon maps
M. S. Gonchenko, A. O. Kazakov, E. A. Samylina +1
We consider reversible non-conservative perturbations of the conservative cubic Hénon maps and study their influence on t…
Homoclinic chaos in the Rössler model
Semyon Malykh, Yuliya Bakhanov, Alexey Kazakov +2
We study the origin of homoclinic chaos in the classical 3D model proposed by O. Rössler in 1976. Of our particular interest are the convoluted bifurcations of the Shilnikov saddle…