5 papers
Cascades of Lorenz attractors in the Shimizu-Morioka model
Alexey Kazakov, Vladislav Koryakin, Klim Safonov +1
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property pe…
Robust chaos in a totally symmetric network of four phase oscillators
Efrosiniia Karatetskaia, Alexey Kazakov, Klim Safonov +1
We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged anal…
Analytic proof of the emergence of new type of Lorenz-like attractors from the triple instability in systems with -symmetry
Efrosiniia Karatetskaia, Alexey Kazakov, Klim Safonov +1
We study bifurcations of a symmetric equilibrium state in systems of differential equations invariant with respect to a -symmetry. We prove that if the equilibrium st…
Multi-winged Lorenz attractors due to bifurcations of a periodic orbit with multipliers
Efrosiniia Karatetskaia, Alexey Kazakov, Klim Safonov +1
We show that bifurcations of periodic orbits with multipliers can lead to the birth of pseudohyperbolic (i.e., robustly chaotic) Lorenz-like attractors of three differe…
Reversible perturbations of conservative Hénon-like maps
M. S. Gonchenko, S. V. Gonchenko, K. Safonov
For area-preserving Hénon-like maps and their compositions, we consider smooth perturbations that keep the reversibility of the initial maps but destroy their conservativity. For c…