Time-delay-induced phase-transition to synchrony in coupled bursting neurons

Signal transmission time delays in a network of nonlinear oscillators are known to be responsible for a variety of interesting dynamic behaviors including phase-flip transitions leading to synchrony or out of synchrony. Here, we uncover that phase-flip transitions are general phenomena and can occur in a network of coupled bursting neurons with a variety of coupling types. The transitions are marked by nonlinear changes in both temporal and phase-space characteristics of the coupled system. We demonstrate these phase-transitions with Hindmarsh-Rose and Leech-Heart interneuron models and discuss the implications of these results in understanding collective dynamics of bursting neurons in the brain.     

Propagation of vector solitons in a quasi-resonant medium with stark deformation of quantum states

The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces ?? transitions, while the extraordinary component induces the ?? transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.     

Quantum coherent control of two-photon transitions by square phase-modulation

A femtosecond laser pulse can be tailored to control the two-photon transitions using the ultra-fast pulse-shaping technique. This paper theoretically and experimentally demonstrates that two-photon transitions in molecular system with broad absorption line can be effectively controlled by square phase-modulation in frequency domain, and the influence of all parameters characterizing the square phase-modulation on two-photon transitions is systemically investigated and discussed. The obtained results have potential application in nonlinear spectroscopy and molecular physics.     

Heterogeneous recurrence representation and quantification of dynamic transitions in continuous nonlinear processes

Many real-world systems are evolving over time and exhibit dynamical behaviors. In order to cope with system complexity, sensing devices are commonly deployed to monitor system dynamics. Online sensing brings the proliferation of big data that are nonlinear and nonstationary. Although there is rich information on nonlinear dynamics, significant challenges remain in realizing the full potential of sensing data for system control. This paper presents a new approach of heterogeneous recurrence analysis for online monitoring and anomaly detection in nonlinear dynamic processes. A partition scheme, named as Q-tree indexing, is firstly introduced to delineate local recurrence regions in the multi-dimensional continuous state space. Further, we design a new fractal representation of state transitions among recurrence regions, and then develop new measures to quantify heterogeneous recurrence patterns. Finally, we develop a multivariate detection method for on-line monitoring and predictive control of process recurrences. Case studies show that the proposed approach not only captures heterogeneous recurrence patterns in the transformed space, but also provides effective online control charts to monitor and detect dynamical transitions in the underlying nonlinear processes.     

Coupled phase transitions under periodic perturbation

The influence of periodic perturbation on the system of two nonlinear stochastic equations, which model low-frequency pulsations in crisis and transient modes of heat-and-mass transfer with phase transitions, has been investigated by numerical methods. When studying the influence of the periodic perturbation on the system, a researcher should largely take into account the phase diagram. It is shown that nonequilibrium phase transitions from asymmetric cycles of phase trajectories to centrally symmetric ones occur in the absence of noise. These transitions are accompanied by the stochastic resonance response, which enhances as the frequency of the external periodic force decreases.     

High frequency forcing on nonlinear systems

High-frequency signals are pervasive in many science and engineering fields.In this work,the effect of high-frequency driving on general nonlinear systems is investigated,and an effective equation for slow motion is derived by extending the inertial approximation for the direct separation of fast and slow motions.Based on this theory,a high-frequency force can induce various phase transitions of a system by changing its amplitude and frequency.Numerical simulations on several nonlinear oscillator systems show a very good agreement with the theoretic results.These findings may shed light on our understanding of the dynamics of nonlinear systems subject to a periodic force.     

Electromagnetic transitions between rydberg states of a hydrogen atom: Violation of the dipole selection rules in a strong field

One-quantum bound-bound transitions between high-excited states of a hydrogen atom are considered. Electron wave functions involving an electromagnetic field even in a zero-order approximation are constructed semiclassically. With these functions, it is shown that transitions accompanied by violation of the dipole selection rules are possible in strong fields. The probability of such transitions is a nonlinear function of electromagnetic field intensity.     

Controlled hysteresis in optical systems surrounded by two feedback loops

The absorptive bistability in a nonlinear optical system surrounded by two feedback loops is studied. The role of the nonlinear element is played by a cell with Λ-type atom vapors placed in a unidirectional ring cavity. The feedback includes two electromagnetic fields interacting with two atomic transitions. A two-dimensional domain of stability was found in the coordinates of field intensities at the input. The dependence of its shape on the values of different parameters of the optical system is studied. The input-output curves corresponding to different trajectories in the domain of stability are obtained.     

Analysis of dynamic pattern formation in nonlinear Fabry-Perot resonators

We present a detailed analysis of transverse effects and pattern formation in bistable optical elements. The system we investigate consists of a Fabry-Perot resonator for the optical feedback element with a nematic liquid-crystal cell used as an optically nonlinear intracavity medium. On illumination with a cw-laser beam, the system causes the beam to break up into several individual spots, passing through several transitions before finally reaching a stationary state. We devise a theoretical model which is used as the basis for numerical simulations of the system. The simulation results are in good agreement with experiment. Finally, we characterize the principal instability of the system using a linear stability analysis of the theoretical model.     

Optical anisotropy of a donor in ellipsoidal quantum dots

A system of an electron with a hydrogenic impurity confined in anisotropic quantum dots with ellipsoidal shape has been investigated. The linear and nonlinear optical absorptions as well as refractive index changes associated with intersubband transitions has been calculated. The results are presented as a function of the incident photon energy. The results show that the optical properties of a donor in ellipsoidal quantum dots are strongly affected by the anisotropy degree and the dot size. The dot anisotropy is shown to play a fundamental role in determining the dot properties.     

Complex patterns in reaction-diffusion systems: A tale of two front instabilities

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatiotemporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.     

Electroconvection of a poorly conducting fluid in a steady electric field

The emergence of electroconvection and nonlinear flows of a nonisothermal poorly conducting fluid in a steady electric field of a horizontal capacitor is investigated. The main mechanism of charge formation in the fluids under investigation is electric conduction due to the temperature dependence of the charge mobility. The Galerkin method is used for obtaining a system of nonlinear differential equations for the amplitudes of spatial modes; on the basis of this system, steady-state, periodic, and random nonlinear regimes of the fluid flow are investigated. The scenarios of transition to chaotic flows (via intermittence and a subharmonic cascade) are discovered. The interrelation between the electroconductive and thermogravitational mechanisms of convection is analyzed, and hysteretic transitions between monotonic and oscillatory regimes are studied. Qualitative comparison with the experiment is carried out.     

统计物理的微观动力学基础

统计的基本出发点是研究系统具有的随机性,不同系统在不同情形下的宏观热力学性质起源于系统内部随机性的差异,通过对宏观热力学系统的微观非线性动力学进行研究探索，我们可以进一步更为深入地理解物态方程、相变等诸多的宏观热力学现象。本文通过哈密顿系统的非线性动力学研究，以及遍历性理论的动力学随机性研究对此问题进行了分析，研究表明，动力学系统的全局性混沌是系统统计成立的根本要素，系统的无限大自由度（热力学极限）已不是决定性的因素，人们可以在此基础上建立少自由度系统的统计力学及热力学。     

Order parameter analysis of synchronization transitions on star networks

The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations, by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe–Strogatz transformation, Ott–Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.     

Coherent Control of Absorption Resonances via Antirotating Coupling

Effects of the antirotating coupling on the absorption resonances are presented for a microwave driven three-level system. It is shown that nonlinear sideband generation, selective suppression and switching between peaks and dips in the absorption spectrum are obtained as the microwave Rabi frequency is varied. A physical explanation is given in terms of the coherent superposition of an infinite set of transitions that are associated with an infinite set of dressed states, which are created by the rotating and nonrotating couplings as the equivalent bichromatic excitation.     

Chaos and self-organization in an open nonconservative system of two plane coplanar magnetized bodies with moments of inertia

Numerical analysis is used to study the nonlinear oscillation processes in an open nonconservative system of two plane coplanar magnetized bodies with moments of inertia. Bifurcation diagrams that illustrate different dynamic regimes of the system in an oscillating magnetic field, as well as the possibility of transitions from one regime to another due to variations in the parameters of the external action, are obtained. It is established that, for the regimes corresponding to infinite phase trajectories, in the general case, an asymmetry occurs in the choice of the rotation direction of the magnetized bodies.     

Growth and Nonlinear Saturation of Fluctuations in a Nonlinear Oscillator at the Threshold of a Bifurcation of Spontaneous Symmetry Breaking

We consider the phenomenon of prebifurcation noise amplification in a nonlinear oscillator at the threshold of a bifurcation of spontaneous symmetry breaking. The studies are based on the model of a nonlinear oscillator in which the potential relief transforms from monostable to symmetric bistable and the noise acting on the system is assumed Gaussian and short-correlated. The fluctuation variance as a function of the regime of the system and the rate at which the bifurcation threshold is reached are examined. Our analytical estimates are in good agreement with the results of numerical simulation for both the linear growth and the nonlinear saturation of fluctuations. It is noted that in the case of fast bifurcation transitions, a loop of noise-dependent hysteresis and breaking of probability symmetry of stable final states are observed in the nonlinear oscillator. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 425–435, May 2005.     

Intricate evolutions of multiple-period post-buckling patterns in bilayers

Surface instability of compliant film/substrate bilayers has raised considerable interests due to its broad applications such as wrinkle-driven surface renewal and antifouling,shape-morphing for camouflaging skins,and micro/nano-scale surface patterning control.However,it is still a challenge to precisely predict and continuously trace secondary bifurcation transitions in the nonlinear post-buckling region.Here,we develop lattice models to precisely capture the nonlinear morphology evolution with multiple mode transitions that occur in the film/substrate systems.Based on our models,we reveal an intricate post-buckling phenomenon involving successive flat-wrinkle-doubling-quadrupling-fold bifurcations.Pre-stretch and pre-compression of the substrate,as well as bilayer modulus ratio,can alter surface morphology of film/substrate bilayers.With high substrate pre-tension,hierarchical wrinkles emerge in the bilayer with a low modulus ratio,while a wrinkle-to-ridge transition occurs with a high modulus ratio.Besides,with moderate substrate pre-compression,the bilayer eventually evolves into a period-tripling mode.Phase diagrams based on neo-Hookean and Arruda-Boyce constitutions are drawn to characterize the influences of different factors and to provide an overall view of ultimate pattern formation.Fundamental understanding and quantitative prediction of the nonlinear morphological transitions of soft bilayer materials hold potential for multifunctional surface regulation.     

Transient dynamics in a small ensemble of synaptically coupled Morris-Lecar neurons

We propose a new model of synaptic transmission on the basis of a FitzHugh–Nagumo system with nonlinear recovery. It is shown that the Morrice–Lecar neuron ensemble formed by such couplings shows various structurally stable regimes of transient dynamics in the form of sequential transitions between various metastable oscillatory states of the system.