混沌动力学
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…
It was demonstrated in [Phys. Rev. E 86, 021104, (2012)], that the ground-state wave functions for a large variety of one-dimensional spin-1/2 models are multifractals in the natural spin-z basis. We present here the details of analytical…
In contrast to the claim of Motter and Campbell on Chaos at Fifty, done at arXiv:1306.5777, it is pointed out that in 2013 we are at Chaos Fifty Four, if to count correctly and to remember about pioneering results of Boris Chirikov obtained…
Here we extend a recent review (Physics Reports {\bf 521}, 205 (2012)) of amplitude death, namely the suppression of oscillations due to the coupling interactions between nonlinear dynamical systems. This is an important emergent phenomenon…
We propose a method to identify and to locate "repellers'' in quasi-periodically forced logistic map (QPLM), using a kind of Morse decomposition of nested attracting invariant sets. In order to obtain the invariant sets, we use an auxiliary…
We propose a population model for $\delta$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term.…
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…
Derivatives of fractional order with respect to time describe long-term memory effects. Using nonlinear differential equation with Caputo fractional derivative of arbitrary order $\alpha>0$, we obtain discrete maps with power-law memory.…
A dynamics of a low-dimensional ensemble consisting of connected in a network five discrete phase oscillators is considered. A two-parameter synchronization picture which appears instead of the Arnold tongues with an increase of the system…
One of the most famous problems in mathematics is the Riemann hypothesis: that the non-trivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as…
This paper is devoted to the investigation of the origin and mechanism of randomization in late boundary layer transition over a flat plate without pressure gradient. The flow randomization is a crucial phase before flow transition to the…
We demonstrated experimentally canard induced mixed mode oscillations (MMO) in an excitable glow discharge plasma, and the results are validated through numerical solution of the FitzHugh Nagumo (FHN) model. When glow discharge plasma is…
In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an unimodal function. We proof a theorem which states the necessary and sufficient…
The mechanism of randomization in late boundary layer transition is a key issue of late boundary layer transition and turbulence theory. We studied the mechanism carefully by high order DNS. The randomization was originally considered as a…
Electric drive using dc shunt motor or permanent magnet dc (PMDC) motor as prime mover exhibits bifurcation and chaos. The characteristics of dc shunt and PMDC motors are linear in nature. These motors are controlled by pulse width…
While musical performances are determined by many factors such as the musical genre and interpretation, rhythmic synchronization is at the foundation of musical interaction. Here, we study the statistical nature of the mutual interaction of…
In linearly stable shear flows turbulence spontaneously decays with a characteristic lifetime that varies with Reynolds number. The lifetime sharply increases with Reynolds number so that a possible divergence marking the transition to…
Structure of bifurcation diagram in the plane of parameters controlling period-doublings for the system of coupled logistic maps is discussed. The analysis is carried out by computing the charts of dynamical regimes and charts of Lyapunov…
We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…
We derive the Hamiltonian structure of the modified Hasegawa-Mima equation from the ion fluid equations applying Dirac's theory of constraints. We discuss the Casimirs obtained from the corresponding Poisson structure.