Virtual Photon Effects on Chaos in Generalized Lorenz-Haken Equation

The dynamics of an ensemble of two-level atoms injected into a single-mode cavity is studied in the exact atom-field interaction situation, in which the counter-rotating terms describing the so-called virtual photon processes neglected in the rotating-wave approximation, are considered. The cavity mode is driven by the injected classical field,and the atom is prepared in a coherent superposition of the two levels. We first derive the generalized Lorenz-Haken equation by using the technique of quantum Langevin equation, and then numerically study the dynamics of this equation.We find that the virtual photon processes have strong effects on the dynamics, which can cause the trajectory in phase space of strange attractor spiral around four focus points, and the trajectory is modulated by virtual photon processes.The chaos region in parameter space is now enlarged. It should be stressed that the strange attractor can exist in optical bistability, and whether the atomic coherences and classical field can inhibit chaos depends on the laser frequency.     

一混沌模型系综模拟研究

有随机模拟方法研究了化学昆沌模型的介观动力学。对该混沌模型的系综模拟发现,在这种不稳定运动中存在强烈的内部涨落,然而由于混沌运动整体上的稳定性,使得系综中的代表点被限制在混沌吸引子上,并且单个代表点形成的随机轨道很好地保持了确定性混沌吸引子的基本特征。     

一混沌模型的系综模拟研究

本文用随机模拟方法研究了一化学混沌模型的介观动力学。对该混沌模型的系综模拟发现 ,在这种不稳定运动中存在强烈的内部涨落 ,然而由于混沌运动整体上的稳定性 ,使得系统中的代表点被限制在混沌吸引子上 ,并且每个代表点形成的随机轨道很好地保持了确定性混沌吸引子的基本特性     

Corticonic models of brain mechanisms underlying cognition and intelligence

The concern of this review is brain theory or more specifically, in its first part, a model of the cerebral cortex and the way it: (a) interacts with subcortical regions like the thalamus and the hippocampus to provide higher-level-brain functions that underlie cognition and intelligence, (b) handles and represents dynamical sensory patterns imposed by a constantly changing environment, (c) copes with the enormous number of such patterns encountered in a lifetime by means of dynamic memory that offers an immense number of stimulus-specific attractors for input patterns (stimuli) to select from, (d) selects an attractor through a process of “conjugation” of the input pattern with the dynamics of the thalamo–cortical loop, (e) distinguishes between redundant (structured) and non-redundant (random) inputs that are void of information, (f) can do categorical perception when there is access to vast associative memory laid out in the association cortex with the help of the hippocampus, and (g) makes use of “computation” at the edge of chaos and information driven annealing to achieve all this. Other features and implications of the concepts presented for the design of computational algorithms and machines with brain-like intelligence are also discussed. The material and results presented suggest, that a Parametrically Coupled Logistic Map network (PCLMN) is a minimal model of the thalamo–cortical complex and that marrying such a network to a suitable associative memory with re-entry or feedback forms a useful, albeit, abstract model of a cortical module of the brain that could facilitate building a simple artificial brain.

In the second part of the review, the results of numerical simulations and drawn conclusions in the first part are linked to the most directly relevant works and views of other workers. What emerges is a picture of brain dynamics on the mesoscopic and macroscopic scales that gives a glimpse of the nature of the long sought after brain code underlying intelligence and other higher level brain functions.     

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.     

Virtual Photon Effects on Chaos in Generalized Lorenz-Haken Equation

The dynamics of an ensemble of two-level atoms injected into a single-mode cavity is studied in the exact atom-field interaction situation, in which the counter-rotating terms describing the so-called virtual photon processes neglected in the rotating-wave approximation, are considered. The cavity mode is driven by the injected classical field,and the atom is prepared in a coherent superposition of the two levels. We first derive the generalized Lorenz-Haken equation by using the technique of quantum Langevin equation, and then numerically study the dynamics of this equation.We find that the virtual photon processes have strong effects on the dynamics, which can cause the trajectory in phase space of strange attractor spiral around four focus points, and the trajectory is modulated by virtual photon processes.The chaos region in parameter space is now enlarged. It should be stressed that the strange attractor can exist in optical bistability, and whether the atomic coherences and classical field can inhibit chaos depends on the laser frequency.     

Classical chaos with Bose-Einstein condensates in tilted optical lattices

A widely accepted definition of "quantum chaos" is "the behavior of a quantum system whose classical limit is chaotic." The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical counterparts. A fundamental reason for that is the linearity of Schr?dinger equation. In this paper, we study the quantum dynamics of an ultracold quantum degenerate gas in a tilted optical lattice and show that it displays features very close to classical chaos. We show that its phase space is organized according to the Kolmogorov-Arnold-Moser theorem.     

An agent-based model of collective emotions in online communities

We develop an agent-based framework to model the emergence of collective emotions, which is applied to online communities. Agent’s individual emotions are described by their valence and arousal. Using the concept of Brownian agents, these variables change according to a stochastic dynamics, which also considers the feedback from online communication. Agents generate emotional information, which is stored and distributed in a field modeling the online medium. This field affects the emotional states of agents in a non-linear manner. We derive conditions for the emergence of collective emotions, observable in a bimodal valence distribution. Dependent on a saturated or a superlinear feedback between the information field and the agent’s arousal, we further identify scenarios where collective emotions only appear once or in a repeated manner. The analytical results are illustrated by agent-based computer simulations. Our framework provides testable hypotheses about the emergence of collective emotions, which can be verified by data from online communities.     

Chaotic itinerancy in the oscillator neural network without Lyapunov functions

Chaotic itinerancy (CI), which is defined as an incessant spontaneous switching phenomenon among attractor ruins in deterministic dynamical systems without Lyapunov functions, is numerically studied in the case of an oscillator neural network model. The model is the pseudoinverse-matrix version of the previous model [S. Uchiyama and H. Fujisaka, Phys. Rev. E 65, 061912 (2002)] that was studied theoretically with the aid of statistical neurodynamics. It is found that CI in neural nets can be understood as the intermittent dynamics of weakly destabilized chaotic retrieval solutions.     

de Broglie-Bohm formulation of quantum mechanics, quantum chaos and breaking of time-reversal invariance

A recently developed unified theory of classical and quantum chaos, based on the de Broglie-Bohm (Hamilton-Jacobi) formulation of quantum mechanics is presented and its consequences are discussed. The quantum dynamics is rigorously defined to be chaotic if the Lyapunov number, associated with the quantum trajectories in de Broglie-Bohm phase space, is positive definite. This definition of quantum chaos which under classical conditions goes over to the well-known definition of classical chaos in terms of positivity of Lyapunov numbers, provides a rigorous unified definition of chaos on the same footing for both the dynamics. A demonstration of the existence of positive Lyapunov numbers in a simple quantum system is given analytically, proving the existence of quantum chaos. Breaking of the time-reversal symmetry in the corresponding quantum dynamics under chaotic evolution is demonstrated. It is shown that the rigorous deterministic quantum chaos provides an intrinsic mechanism towards irreversibility of the Schrodinger evolution of the wave function, without invoking ‘wave function collapse’ or ‘measurements’     

Relation of a New Interpretation of Stochastic Differential Equations to Ito Process

Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed. Different interpretations specify different dynamics. Recently, a new interpretation of SDE is put forward by one of us. This interpretation has a built-in Boltzmann-Gibbs distribution and shows the existence of potential function for general processes, which reveals both local and global dynamics. Despite its powerful property, its relation with classical ones in arbitrary dimension remains obscure. In this paper, we will clarify such connection and derive the concise relation between the new interpretation and Ito process. We point out that the derived relation is experimentally testable.     

Noise induced complexity: from subthreshold oscillations to spiking in coupled excitable systems

We study the stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. In the course of this transition diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed. In order to understand the details and mechanisms of these noise-induced dynamics we consider the thermodynamic limit N-->infinity of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good qualitative agreement with dynamical scenarios observed in the stochastic simulations of large ensembles.     

Evolution of order and chaos across a first-order quantum phase transition

We study the evolution of the dynamics across a generic first-order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis reveals a robustly regular dynamics confined to the deformed region and well separated from a chaotic dynamics ascribed to the spherical region. A quantum analysis discloses regular bands of states in the deformed region, which persist to energies well above the phase-separating barrier, in the face of a complicated environment. The impact of kinetic collective rotational terms on this intricate interplay of order and chaos is investigated.     

Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties

We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition probabilities between different nodes of the network. We derive a relation between the entropy and the spectrum of the master equation’s transfer matrix. Our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling. In analogy to chaos theory, the proportionality factor is called (stochastic) information dimension and gives a global characterization of the dynamics on the network. These general results are corroborated by examples of regular and of fractal networks.     

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Ro?ssler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.     

Dynamical entropy production in spiking neuron networks in the balanced state

We demonstrate deterministic extensive chaos in the dynamics of large sparse networks of theta neurons in the balanced state. The analysis is based on numerically exact calculations of the full spectrum of Lyapunov exponents, the entropy production rate, and the attractor dimension. Extensive chaos is found in inhibitory networks and becomes more intense when an excitatory population is included. We find a strikingly high rate of entropy production that would limit information representation in cortical spike patterns to the immediate stimulus response.     

Coherent states and path integrals for model hamiltonians in quantum optics

A brief review of applications of the coherent states (CSes) in quantum optics is given. The CS representation of path integrals in the semi-classical approximation leads to the classical dynamics of CS parameters. Calculations of squeezing in the model of spontaneous parametric scattering are performed and the chaos in the collective dynamics of three-level atoms interacting with resonant photon modes is studied.     

Intentional systems: Review of neurodynamics, modeling, and robotics implementation

We present an intentional neurodynamic theory for higher cognition and intelligence. This theory provides a unifying framework for integrating symbolic and subsymbolic methods as complementary aspects of human intelligence. Top-down symbolic approaches benefit from the vast experience with logical reasoning and with high-level knowledge processing in humans. Connectionist methods use bottom-up approach to generate intelligent behavior by mimicking subsymbolic aspects of the operation of brains and nervous systems. Neurophysiological correlates of intentionality and cognition include sequences of oscillatory patterns of mesoscopic neural activity. Oscillatory patterns are viewed as intermittent representations of generalized symbol systems, with which brains compute. These dynamical symbols are not rigid but flexible. They disappear soon after they emerged through spatio-temporal phase transitions. Intentional neurodynamics provides a solution to the notoriously difficult symbol grounding problem. Some examples of implementations of the corresponding dynamic principles are described in this review.     

基于比例积分控制的电压反馈型Buck变换器分岔

在分段光滑模型的基础上,推导出基于比例积分(PI)控制的电压反馈型Buck变换器的光滑模型及离散迭代模型.证明了功率系统的混沌吸引子在负载线上运动,并受到占空比的控制,模型的流形围绕吸引子运动并出现1周期、2周期及混沌现象;推导出电压反馈型PI控制系统的输出电压与Buck变换器的输出电压成线性关系,在此基础上指出PI控制中的比例因子起主导作用;分析了系统的倍周期分岔、边界碰撞和混沌现象,并展示了变换器状态的转移过程.实验结果表明了理论建模分析和仿真的正确性.