56 citations · 79 across the 10 of their papers we have counts for
11 papers
Appearance of discrete Lorenz attractors in the transitions from saddle to saddle-focus
Ivan Ovsyannikov
Triply degenerate fixed points appear in global bifurcations -- homoclinic and heteroclinic tangencies. In order to get Lorenz-like attractors, the dynamics of the first return map…
Classification of Codimension-1 Singular Bifurcations in Low-dimensional DAEs
Ivan Ovsyannikov, Haibo Ruan
The study of bifurcations of differential-algebraic equations (DAEs) is the topic of interest for many applied sciences, such as electrical engineering, robotics, etc. While some o…
Global and local bifurcations, three-dimensional Henon maps and discrete Lorenz attractors
Ivan Ovsyannikov
Lorenz attractors play an important role in the modern theory of dynamical systems. The reason is that they are robust, i.e. preserve their chaotic properties under various kinds o…
On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps
M. Gonchenko, S. V. Gonchenko, I. Ovsyannikov +1
We study the 1:4 resonance for the conservative cubic Hénon maps with positive and negative cubic term. These maps show up different bifurcation structures both fo…
On birth of discrete Lorenz attractors under bifurcations of 3D maps with nontransversal heteroclinic cycles
Ivan Ovsyannikov
Lorenz attractors are important objects in the modern theory of chaos. The reason from one side is that they are met in various natural applications (fluid dynamics, mechanics, las…
Bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps
Marina Gonchenko, Sergey V. Gonchenko, Ivan Ovsyannikov
We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different firs…
Homoclinic tangencies to resonant saddles and discrete Lorenz attractors
S. V. Gonchenko, I. I. Ovsyannikov
We study bifurcations of periodic orbits in three parameter general unfoldings of certain types quadratic homoclinic tangencies to saddle fixed points. We apply the rescaling techn…
On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node
S. V. Gonchenko, O. V. Gordeeva, V. I. Lukjanov +1
We study main bifurcations of multidimensional diffeomorphisms having a non-transversal homoclinic orbit to a saddle-node fixed point. On a parameter plane we build a bifurcation d…
Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points
S. V. Gonchenko, I. I. Ovsyannikov, J. C. Tatjer
It was established in 2006 that bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a saddle-focus fixed point with the Jacobian equal to 1 can lead to…
Bifurcation to Chaos in the complex Ginzburg-Landau equation with large third-order dispersion
I. I. Ovsyannikov, D. Turaev, S. Zelik
We give an analytic proof of the existence of Shilnikov chaos in complex Ginzburg-Landau equation subject to a large third-order dispersion perturbation.
Chaotic dynamics of three-dimensional Hénon maps that originate from a homoclinic bifurcation
S. V. Gonchenko, J. D. Meiss, I. I. Ovsyannikov
We study bifurcations of a three-dimensional diffeomorphism, , that has a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers $(λe^{i\vphi}, λe^{-i\vp…