混沌动力学
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
Birhythmicity arises in several physical, biological and chemical systems. Although, many control schemes are proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the…
We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual…
We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal in- variance. On the basis of our data sets we…
We introduce the concepts of perpetual points and periodic perpetual loci in discrete--time systems (maps). The occurrence and analysis of these points/loci are shown and basic examples are considered. We discuss the potential usage and…
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic…
Superconducting QUantum Interference Device (SQUID) metamaterials are superconducting artificial media whose function relies both on their geometry and the extraordinary properties of superconductivity and the Josephson effect. Recent…
Chimera is a relatively new emerging phenomenon where coexistence of synchronous and asynchronous state is observed in symmetrically coupled dynamical units. We report observation of the chimera state in multiplex networks where individual…
In this paper we qualitatively analyse quadratically damped oscillators with non-linear restoring force. In particular, we obtain Hamiltonian structure and analytical form of the energy functions.
We consider the system of two material points that interact by elastic forces according to Hooke's law and their motion is restricted to certain curves lying on the plane. The nonintegrability of this system and idea of the proof are…
Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of…
Exact analytical expressions for the cross-section correlation functions of chaotic scattering sys- tems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are…
We explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which…
We study numerically a system of two lasers cross-coupled optoelectronically with a time delay where the output intensity of each laser modulates the pump current of the other laser. We demonstrate control of chaos via variable coupling…
Statistical properties for the recurrence of particles in an oval billiard with a hole in the boundary are discussed. The hole is allowed to move in the boundary under two different types of motion: (i) counterclockwise periodic circulation…
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…
We examine the multiscaling behavior of the normal- and superfluid-velocity structure functions in three-dimensional superfluid turbulence by using a shell model for the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK)…
A few-degrees-of-freedom Hamiltonian model exhibiting one-directional long-term trends in energy exchange flows is introduced. The model includes a massive potential well - a container with one or few relatively light non-interacting…
The periodic motion of a classical point particle in a one-dimensional double-well potential acquires a surprising degree of complexity if friction is added. Finite uncertainty in the initial state can make it impossible to predict in which…
The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and…