混沌动力学
We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color…
This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use…
We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known…
We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the…
We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the…
We propose new methods to numerically approximate non-attracting sets governing transiently-chaotic systems. Trajectories starting in a vicinity $\Omega$ of these sets escape $\Omega$ in a finite time $\tau$ and the problem is to find…
The results of this study are continuation of the research of Poincar\'e chaos initiated in papers (Akhmet M, Fen MO. Commun Nonlinear Sci Numer Simulat 2016;40:1-5; Akhmet M, Fen MO. Turk J Math, doi:10.3906/mat-1603-51, accepted). We…
For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling…
In the present work we study the Fermi--Pasta--Ulam (FPU) $\beta $--model involving long--range interactions (LRI) in both the quadratic and quartic potentials, by introducing two independent exponents $\alpha_1$ and $\alpha_2$…
The study of PT-symmetric physical systems began in 1998 as a complex generalization of conventional quantum mechanics, but beginning in 2007 experiments began to be published in which the predicted PT phase transition was clearly observed…
This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control…
We investigate spatio-temporal dynamics of a 2D ensemble of nonlocally coupled chaotic cubic maps in a bistability regime. In particular, we perform a detailed study on the transition "coherence -- incoherence" for varying coupling strength…
The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their…
We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show…
In this paper we present an analytical study on the synchronization dynamics observed in unidirectionally-coupled quasiperiodically-forced systems that exhibit Strange Non-chaotic Attractors (SNA) in their dynamics. The SNA dynamics…
The energy transition towards an increased supply of renewable energy raises concerns that existing electricity grids, built to connect few centralized large power plants with consumers, may become more difficult to control and stabilized…
Topological techniques are powerful tools for characterizing the complexity of many dynamical systems, including the commonly studied area-preserving maps of the plane. However, the extension of many topological techniques to higher…
The dynamics of the convergence to the critical attractor for the logistic map is investigated. At the border of chaos, when the Liapunov exponent is zero, the use of the non-extensive statistical mechanics formalism allows to define a weak…
We investigate the connection between local and global dynamics of two N-degree of freedom Hamiltonian systems with different origins describing one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a discretized version…
We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…