Synchronization of time-continuous chaotic oscillators

Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded in the fully synchronized state lose their transverse stability, and the appearance of globally and locally riddled basins of attraction is discussed, respectively, in terms of the subcritical, supercritical nature of the riddling bifurcations. We show how the introduction of a small parameter mismatch between the interacting chaotic oscillators causes a shift of the synchronization manifold. The presence of a coupling asymmetry is found to lead to further modifications of the destabilization process. Finally, the paper considers the problem of partial synchronization in a system of four coupled R?ssler oscillators.     

Quantum chemistry of the bipolaron in an isotropic continuous medium

We consider the electronic wave functions and binding energy of the bipolaron, which is a bound state of two electrons in an ionic crystal. The system is considered in terms of a model resembling the helium atom or hydrogen molecule, where the role of the attractive Coulomb potentials of the nuclei is played by polarization potential wells calculated in the macroscopic approximation. The importance of correlations in the motion of the electrons in the bipolaron is demonstrated. An existence criterion for the bipolaron is established and its binding energy and characteristic size is determined. We also consider quasimolecules formed in a polarizable medium from like-charged particles of different masses (such as an electron plus a^– meson).Deceased.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 6, pp. 641–647, November–December, 1989.     

Noise-induced switching in two adaptively coupled excitable systems

We demonstrate that the interplay of noise and plasticity gives rise to slow stochastic fluctuations in a system of two adaptively coupled active rotators with excitable local dynamics. Depending on the adaptation rate, two qualitatively different types of switching behavior are observed. For slower adaptation, one finds alternation between two modes of noise-induced oscillations, whereby the modes are distinguished by the different order of spiking between the units. In case of faster adaptation, the system switches between the metastable states derived from coexisting attractors of the corresponding deterministic system, whereby the phases exhibit a bursting-like behavior. The qualitative features of the switching dynamics are analyzed within the framework of fast-slow analysis.     

Particle on surface: 3D-effects in dry laser cleaning

Previous analysis of dry laser cleaning within the frame of a one-dimensional (1D) model with homogeneous surface heating shows that this model disagrees with experiments by one–two orders of magnitude. The particle on the surface produces an inhomogeneous intensity distribution in its vicinity due to scattering and diffraction. This produces a nonstationary 3D distribution of the temperature and nonstationary 3D thermal deformations of the surface. If one uses the Mie theory for calculation of inhomogeneous intensity then in some region of the parameters, the 3D model predicts results close to the experimental ones. The next step was done when the scattering effects for radiation reflected from the surface was taken into account (so-called “particle on surface” problem). This approach yields results close to the experimental one within the wide range of parameters. PACS 42.25.Fx; 42.25.Hz; 81.65.CfAn erratum to this article can be found at .     

Properties of stationary states of delay equations with large delay and applications to laser dynamics

We consider properties of periodic solutions of the differential‐delay system, which models a laser with optical feedback. In particular, we describe a set of multipliers for these solutions in the limit of large delay. As a preliminary result, we obtain conditions for stability of an equilibrium of a generic differential‐delay system with fixed large delay τ. We also show a connection between characteristic roots of the equilibrium and multipliers of the mapping obtained via the formal limit τ→∞. Copyright © 2004 John Wiley & Sons, Ltd.     

Eckhaus instability in systems with large delay

The dynamical behavior of various physical and biological systems under the influence of delayed feedback or coupling can be modeled by including terms with delayed arguments in the equations of motion. In particular, the case of long delay may lead to complicated and high-dimensional dynamics. We investigate the effects of delay in systems that display an oscillatory instability (Hopf bifurcation) in the absence of delay. We show by analytical and numerical methods that the dynamical scenario includes the coexistence of multiple stable periodic solutions and can be described in terms of the Eckhaus instability, which is well known in the context of spatially extended systems.     

Two-cluster bifurcations in systems of globally pulse-coupled oscillators

For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all stationary two-cluster states and explain how the different states are naturally connected via bifurcations. The coupling is modeled using the phase-response-curve (PRC), which measures the sensitivity of each oscillator’s phase to perturbations. For large systems with a PRC, which is zero at the spiking threshold, we are able to find the parameter regions where multiple stable two-cluster states coexist and illustrate this by an example. In addition, we explain how a locally unstable one-cluster state may form an attractor together with its homoclinic connections. This leads to the phenomenon of intermittent, asymptotic synchronization with abating beats away from the perfect synchrony.     

Defect driven ferroelectricity and magnetism in nanocrystalline KTaO3

Nominally pure nanocrystalline KTaO₃ was thoroughly investigated by micro-Raman and magnetic resonance spectroscopic techniques. In all samples the defect driven ferroelectricity and magnetism are registered. Both ordering states are suggested to appear due to the iron atoms and oxygen vacancies. The concentration of defects was estimated to be 0.04 and 0.06-0.1 mol%. Note that undoped single crystals of KTaO₃ are nonmagnetic and have never exhibited ferromagnetic properties. The results enable us to refer a nanosized KTaO₃ to the class of multiferroics and assume that it could perform the magnetoelectric effect at T<29 K. It was also established that the critical concentration of impurity defects necessary to provoke the appearance of the new phase states in the material strongly correlates with the size of the particle; as the size of the particle decreases, the critical concentration decreases as well.     

Effect of the nucleophile structure and basicity on pyridine-catalyzed formation of thiosemicarbazides

The kinetics of pyridine-catalyzed reaction of O,O-diaryl hydrazidothiophosphates with phenyl isothiocyanate in benzene at 25°C were studies. Pyridine was found to exhibit a considerable catalytic effect in the formation of phosphorus-containing thiosemicarbazides. A correlation between the reactivity of phosphorus hydrazides in the catalytic reaction and their structure was revealed. The catalytic activity of pyridine increases as the basicity of hydrazide decreases. The effects of the substituents in the aromatic rings and the basicity of hydrazides weaken in going from the noncatalytic to catalytic process. The catalysis by pyridine conforms to the general base catalysis pattern.     

Quantitative Evaluation of the Influence of Physicochemical Properties of Solvents on the Kinetics of Formation of Phosphorus-Containing Semicarbazides

The kinetics of the reaction of diphenylphosphinic acid hydrazide with phenyl isocyanate in various solvents at 25°C was studied. The results can be quantitatively correlated with the physicochemical characteristics of solvents using the four-parameter Koppel-Palm equation. This relationship allows quantitative analysis of the solvation effects. The decisive influence on the reaction rate is exerted by the basicity and polarity of solvents. The reaction mechanism is discussed, and the possible scheme of solvation is suggested.