混沌动力学

In this paper we study the evolution of the wave function with the system size in a locally periodic structure. In particular we analyse the dependence of the wave function with the number of unit cells, which also reflects information…

Shuichi Nos\'e opened up a new world of atomistic simulation in 1984. He formulated a Hamiltonian tailored to generate Gibbs' canonical distribution dynamically. This clever idea bridged the gap between microcanonical molecular dynamics and…

Left- and right-handed helical modes' statistical absolute equilibria appear \textit{separately}. If both chiral sectors present, one can dominate around its positive pole, which is relevant to the nearly maximally helical (force free for…

We present an optimization process to estimate parameters in systems of ordinary differential equations from chaotic time series. The optimization technique is based on a variational approach, and numerical studies on noisy time series…

A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…

Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through…

The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…

In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…

We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…

Since Bandt et al. have shown that the permutation entropy and the Kolmogorov-Sinai entropy coincide for piecewise monotone interval maps, the relationship of both entropies for time-discrete dynamical systems is of a certain interest. The…

This work considers reversed evolution in dynamical systems. In particular, asymptotic behavior of chaotic systems, when their orbits evolve backwards in time. Reversed dynamics reveals important aspects of the trajectories, such as a new…

We present a detailed direct numerical simulation of statistically steady, homogeneous, isotropic, two-dimensional magnetohydrodynamic (2D MHD) turbulence. Our study concentrates on the inverse cascade of the magnetic vector potential. We…

We recently analyzed the voltage of the memristic circuit proposed by Muthuswamy and Chua by adding an external sinusoidal oscillation $\gamma\omega \cos\omega t$ to the ${\dot y}(t)\simeq {\dot i_L}(t)$, when the ${\dot x}(t)\simeq {\dot…

In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…

Nonlinear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered and the Poincar\'e map, describing evolution from an impact to the next impact, is described. Displacement of…

Jupiter's fast rotation - one rotation over 10 hours - creates strong jet streams, smearing its clouds into linear bands of dark and light zonal belts that circle the planet on lines of almost constant latitude. Such a high degree of…

Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…

We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes…

In this paper we present an experimental setup and an associated mathematical model to study the synchronization of two self sustained strongly coupled mechanical oscillators (metronomes). The effects of a small detuning in the internal…

High levels of penetration of distributed generation and aggressive reactive power compensation with modern power electronics may result in the reversal of active and reactive power flows in future distribution grids. The voltage stability…