混沌动力学
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and…
The issue of why computational resolution in Navier-Stokes turbulence is so hard to achieve is addressed. It is shown that Navier-Stokes solutions can potentially behave differently in two distinct regions of space-time $\mathbb{R}^{\pm}$…
Weakly non-linear stability of regimes of free hydromagnetic thermal convection in a rotating horizontal layer with free electrically conducting boundaries is considered in the Boussinesq approximation. Perturbations are supposed to involve…
A systematic procedure to derive shell models for MHD turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross-helicity and the magnetic helicity as well as the…
We investigate localization phenomena and stability properties of quasiperiodic oscillations in $N$ degree of freedom Hamiltonian systems and $N$ coupled symplectic maps. In particular, we study an example of a parametrically driven…
We introduce a new definition of distinguished trajectory that generalises the concepts of fixed point and periodic orbit to aperiodic dynamical systems. This new definition is valid for identifying distinguished trajectories with…
The dynamics of the truncated Euler equations with helical initial conditions are studied. Transient energy and helicity cascades leading to Kraichnan helical absolute equilibrium at small scales are obtained for the first time. The results…
The escape rate of a stochastic dynamical system can be found as an expansion in powers of the noise strength. In previous work the coefficients of such an expansion for a one-dimensional map were fitted to a general form containing a few…
We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed in [1,2]. The algorithms for computation of the time averages of observables on phase space are developed and…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is…
Vibrations of the Jeffcott rotor are modelled by a three degree of freedom system including coupling between lateral and torsional modes. The crack in a rotating shaft of the rotor is introduced via time dependent stiffness with off…
The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…
Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have…
We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a…
A three-component dynamic system with influence of pumping and nonlinear dissipation describing a quantum cavity electrodynamic device is studied. Different dynamical regimes are investigated in terms of divergent trajectories approaches…
In this paper we have considered the problem of parametric sound generation in an acoustic resonator flled with a fluid, taking explicitely into account the influence of the nonlinearly generated second harmonic. A simple model is…
We show that rocky shorelines with fractal dimension 4/3 are conformally invariant curves by measuring the statistics of their winding angles from global high-resolution data. Such coastlines are thus statistically equivalent to the outer…
The paper deals with time-scaling transformations of dynamical systems. Such scaling functions operate a change of coordinates on the time axis of the system trajectories preserving its phase portrait. Exploiting this property, a chaos…
We conduct numerical experiments to investigate the spatial clustering of particles and bubbles in simulations of homogeneous and isotropic turbulence. Varying the Stokes parameter and the densities, striking differences in the clustering…