混沌动力学
We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the…
In the studies of plant infections, the plant immune response is known to play an essential role. In this paper we derive and analyse a new mathematical model of plant immune response with particular account for post-transcriptional gene…
A general relation is derived for the action difference between two fixed points and a phase space area bounded by the irreducible component of a heteroclinic tangle. The determination of this area can require accurate calculation of…
In this paper a Lorenz-like system, describing the process of rotating fluid convection, is considered. The present work demonstrates numerically that this system, also like the classical Lorenz system, possesses a homoclinic trajectory and…
In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with…
We study the generalized synchronization and its stability using master stability function (MSF), in a network of coupled nearly identical dynamical systems. We extend the MSF approach for the case of degenerate eigenvalues of the coupling…
We studied correlations between different nodes in small electronic networks with active links operating as jitter generators. Unexpectedly, we found that under certain conditions signals from the most remote nodes in the networks correlate…
Linear augmentation has recently been shown to be effective in targeting desired stationary solutions, suppressing bistablity, in regulating the dynamics of drive response systems and in controlling the dynamics of hidden attractors. The…
We consider two special types of double pendula, with the motion of masses restricted to various surfaces. In order to get quick insight into the dynamics of the considered systems the Poincar\'e cross sections as well as bifurcation…
The old idea that an infinite dimensional dynamical system may have its high modes or frequencies slaved to low modes or frequencies is re-visited in the context of the $3D$ Navier-Stokes equations. A set of dimensionless frequencies…
We propose rotation inferred from the polar decomposition of the flow gradient as a diagnostic for elliptic (or vortex-type) invariant regions in non-autonomous dynamical systems. We consider here two- and three-dimensional systems, in…
The cluster synchronization is a very important characteristic for the higher harmonic coupling Kuramoto system. A novel transformation is provided, and it gives cluster synchronization by the periodic properties of the density function.…
Ghost-stochastic resonance is a noise-induced resonance at a missing fundamental frequency in the input signal. In this paper we investigate the features of ghost-stochastic resonance in a unidirectionally coupled network and small-world…
The motion of point vortices constitutes an especially simple class of solutions to Euler's equation for two dimensional, inviscid, incompressible, and irrotational fluids. In addition to their intrinsic mathematical importance, these…
It is found that Lorenz systems can be unidirectionally coupled such that the chaos expands from the drive system. This is true if the response system is not chaotic, but admits a global attractor, an equilibrium or a cycle. The extension…
The distribution of finite time observable averages and transport in low dimensional Hamiltonian systems is studied. Finite time observable average distributions are computed, from which an exponent $\alpha$ characteristic of how the…
In this paper we categorize dynamical regimes demonstrated by star-like networks with chaotic nodes. This analysis is done in view of further studying of chaotic scale-free networks, since a star-like structure is the main motif of them. We…
We propose an exact analytical formula for the anomalous scaling exponents of inertial range structure functions in incompressible fluid turbulence. The formula is a gravitational Knizhnik-Polyakov-Zamolodchikov (KPZ)-type relation, and is…
The dynamics of a bouncing ball model under the influence of dissipation is investigated by using a two dimensional nonlinear mapping. When high dissipation is considered, the dynamics evolves to different attractors. The evolution of the…
Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of processes the parameter $K$ is chosen at random from a Gaussian…