Fidelity of isotropic-coupled oscillators interacting with a single atom

A model of a single atom interacting with isotropic two modes pumped simultaneously within a perfect cavity is examined. The quantum fidelity is employed to measure the quality of transmitted information as a function of the input state. The behavior of the quantum fidelity is studied at off-resonances between the atom and fields for different preparations of initial states.     

Synchronization in a neural network of phase oscillators with time delayed coupling

We investigate a neural network model designed as a system of the central oscillator and peripheral oscillators interacting with a time delay in a phase-locking loop. The delay corresponds to the finite velocity of signal propagation along nerve fibers. We study the synchronization under various values of . It is shown that under some conditions for a finite delay time there exist a multitude of synchronization frequencies in contrast to the case without delay where one has at most one solution. The criteria for the existence of multiple solutions and their stability are found. The asymptotic behavior under increasing connection strengths is analyzed.Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 8, pp. 945–960, August, 1994.     

小世界生物神经网络的相干共振研究

研究了无外界周期信号时Hodgkin-Huxley模型小世界生物神经网络的非线性响应.数值模拟结果显示：当噪声强度取某一有限值时,峰序列有序度可以达到最大,即产生相干共振现象.同时发现： 随着网络规模N的变化,相干共振系数cv的极小值不是一个,而是多个.这表明相干共振可发生在神经元集群数目特定的不同规模的网络中. 关键词： 相干共振 有序度 小世界网络 生物神经网络     

Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators

A theory of intrinsic fluctuations is developed of a phase ordering parameter for large populations of weakly and uniformly coupled limit-cycle oscillators with distributed native frequencies. In particular it is shown that the intensity as well as the correlation time of fluctuations exhibit power-law divergence at the onset of mutual entrainment with critical exponents which depend on whether the coupling strength approaches the threshold from below or above. This peculiar feature is demonstrated by numerical simulations mainly through finite-size scaling analyses. In the course of exploring its origin, we encounter a new concept termed a correlation frequency which provides a natural interpretation of the finite-size scaling laws. A comment is given on a recent theory by Kuramoto and Nishikawa to clarify why it contradicts our results.     

Quantum aspects of chaos for three-level atoms interacting with two harmonic oscillators

We treat a simple generalization of the Jaynes-Cummings model to three-level atoms interacting with two harmonic oscillators. The model allows for classical chaos even in the rotating wave approximation, as was recently shown by Shepelyanski. Under conditions most favorable for classical chaos we find linear level repulsion à la Wigner.     

Synchronization with an arbitrary phase shift in a pair of synaptically coupled neural oscillators

The phase dynamics of a pair of spiking neural oscillators coupled by a unidirectional nonlinear connection has been studied. The synchronization effect with the controlled relative phase of spikes has been obtained for various coupling strengths and depolarization parameters. It has been found that the phase value is determined by the difference between the depolarization levels of neurons and is independent of the synaptic coupling strength. The synchronization mechanism has been studied by means of the construction and analysis of one-dimensional phase maps. The phase locking effect for spikes has been interpreted in application to the synaptic plasticity in neurobiology.     

Synchronization in a system of globally coupled oscillators with time delay

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results.     

Analysis of a DPSK soliton transmission system

We present a closed form expression to analyse the error performance of a differential phase-shift keying (DPSK) digital modulation format in an optical soliton communication system. In the analysis we include the effect of Gordon-Haus jitter, which is mainly due to the amplified spontaneous emission noise of the amplifiers. Gordon-Haus jitter is found to be less significant when the bit period is 15 times greater than the jitter variance and becomes more significant when the signal-to-noise ratio is greater than 20 dB. Due to a good bit error rate (BER) performance (BER ≈ 10⁻²⁰at SNR= 21 dB), the DPSK modulation format has a potential application for a high-bit-rate and low-noise soliton communication system.     

Signal transmission in two-way coupled neural system: system size effect

We study the collective dynamical behavior of two-way coupled neural system, which is subject to external noise at the first neuron. It is shown that, for smaller system size, coherence resonance without tuning can occur under certain conditions; for larger system size, a critical value of coupling strength is found, which is a threshold for occurrence of array-enhanced coherence resonance and undamped signal transmission. In particular, when system size is increased, it is more efficient to sustain and amplify the internal signal.     

Direction of coupling from phases of interacting oscillators: a permutation information approach

We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy subjects. There is no need for preprocessing and fine-tuning the parameters, which makes the method very simple, computationally fast and robust.     

Breathing chimera in a system of phase oscillators

Chimera states consisting of synchronous and asynchronous domains in a medium of nonlinearly coupled phase oscillators have been considered. Stationary inhomogeneous solutions of the Ott–Antonsen equation for a complex order parameter that correspond to fundamental chimeras have been constructed. The direct numerical simulation has shown that these structures under certain conditions are transformed to oscillatory (breathing) chimera regimes because of the development of instability.     

Dissipation conditions in a system of coupled oscillators

A system of interacting oscillators with a quadratic Hamiltonian is investigated. The necessary and sufficient conditions are determined for the system to exhibit dissipative properties with respect to one designated oscillator. One of the necessary conditions is the existence of a continuous frequency spectrum in the system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 94–98, January, 1988.     

Phase-locking effects in a system of nonlinear oscillators

Models for the excitation of collective modes in a system of nonlinear classical oscillators, initially out of phase, are discussed. The oscillators may be coupled in a dissipative or conservative manner. The analysis is based on the results of recent studies dealing with the problem of the free excitation of a coherent pulse, analogous to "superradiance" in two-level quantum systems. Several physical examples from the realms of electrodynamics and acoustics are discussed. The processes discussed here may be thought of as chaos-order transitions, provided that "chaos" is understood not as a stochastic nature of an individual oscillator but as the absence of a coherent component in their collective field.     

System of interacting harmonic oscillators in rotationally invariant noncommutative phase space

Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of N interacting harmonic oscillators in uniform field and a system of N particles with harmonic oscillator interaction are studied. We analyze effect of noncommutativity on the energy levels of these systems. It is found that influence of coordinates noncommutativity on the energy levels of the systems increases with increasing of the number of particles. The spectrum of N free particles in uniform field in rotationally invariant noncommutative phase space is also analyzed. It is shown that the spectrum corresponds to the spectrum of a system of N harmonic oscillators with frequency determined by the parameter of momentum noncommutativity.     

Photoelectron ionization spectra in a system interacting with a neighbor atom

We study long-time photoelectron ionization spectra of a system interacting with a neighbor two-level atom under the influence of a laser field. The system has at least a ground state and a continuum of states that are free with respect to one electron. In a weak light field, a Fano resonance is revealed. Also we consider an atomic autoionization level of the system, which leads to two Fano resonances under the influence of a weak field.     

Structures of attractors in periodically forced neural oscillators

Periodically forced oscillations in the membrane potential of squid giant axons are analysed by stroboscopic plots at multi-phases of the forcing function. The analysis clarifies the global structures of the attractors in the phase space R² × S¹.