Opinion Dynamics on Networks under Correlated Disordered External Perturbations

We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal and ordered bimodal distribution states, characterized by an increase in the vote-share variability of the equilibrium distributions. The fluctuations (variance and correlations) in the external perturbations are shown to reduce the impact of the external influence by increasing the critical threshold needed for the bimodal distribution of opinions to appear. The external fluctuations also have the surprising effect of driving voters towards biased opinions. Furthermore, the first and second moments of the external perturbations are shown to affect the first and second moments of the vote-share distribution. This is shown analytically in the mean field limit, and confirmed numerically for fully connected networks and other network topologies. Studying the dynamic response of complex systems to disordered external perturbations could help us understand the dynamics of a wide variety of networked systems, from social networks and financial markets to amorphous magnetic spins and population genetics.     

Entropy production and nonequilibrium stationarity in quantum dynamical systems. Physical meaning of van Hove limit

With aid of the so-called dilation method, a concise formula is obtained for the entropy production in the algebraic formulation of quantum dynamical systems. In this framework, the initial ergodic state of an external force system plays a pivotal role in generating dissipativity as a conditional expectation. The physical meaning of van Hove limit is clarified through the scale-changing transformation to control transitions between microscopic and macroscopic levels. It plays a crucial role in realizing the macroscopic stationarity in the presence of microscopic fluctuations as well as in the transition from non-Markovian (groupoid) dynamics to Markovian dissipative processes of state changes. The extension of the formalism to cases with spatial and internal inhomogeneity is indicated in the light of the groupoid dynamical systems and noncommutative integration theory.     

Fluctuations in nonlinear systems near bifurcations corresponding to the appearance of new stable states

Fluctuations in nonlinear multidimensional dynamical systems caused by outer δ-correlated random forces are considered. The slowness of one of the motions at parameter values within the bifurcation region allows us to use the adiabatic approximation and hence to reduce the multidimensional problem to a one-dimensional problem. The exponent and the pre-exponential factor in the expression for the probability of the transition from the metastable equilibrium state of the system are calculated. The kinetics of fluctuations in the systems that are near the bifurcation point where two stable states coincide is considered. The results are illustrated with an example of the Duffing nonlinear oscillator in an external resonance field.     

A study of the dynamical-fluctuation property inside jets in e+e- collisions

A study of the dynamical-fluctuation property of 2-jet events is carried out. It is found that the dynamical fluctuations of the hadronic system inside 2-jet events change with the variation of the cut parameter ycut. There is a transition point, where the dynamical fluctuations in these systems are circular in the transverse plane; and are elliptical in the longitudinal-transverse planes. It is shown that this transition point corresponds to the scale of visible jets. Meanwhile, the dynamical fluctuation properties inside a single-jet in 2-jet and 3-jet events are compared. The dynamical fluctuations inside quark- and gluon-jets are found to be qualitatively different. A scale for the "visible gluon jet" production is thus obtained.     

A study of the dynamical-fluctuation property inside jets in e<Superscript>+</Superscript>e<Superscript>−</Superscript> collisions

A study of the dynamical-fluctuation property of 2-jet events is carried out. It is found that the dynamical fluctuations of the hadronic system inside 2-jet events change with the variation of the cut parameter Y_cut. There is a transition point, where the dynamical fluctuations in these systems are circular in the transverse plane; and are elliptical in the longitudinal-transverse planes. It is shown that this transition point corresponds to the scale of visible jets. Meanwhile, the dynamical fluctuation properties inside a single-jet in 2-jet and 3-jet events are compared. The dynamical fluctuations inside quark- and gluon-jets are found to be qualitatively different. A scale for the “visible gluon jet” production is thus obtained.     

Statistical physics and physiology: monofractal and multifractal approaches.

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.     

Zero-point fluctuations and the quenching of the persistent current in normal metal rings

The ground state of a phase-coherent mesoscopic system is sensitive to its environment. We investigate the persistent current of a ring with a quantum dot which is capacitively coupled to an external circuit with a dissipative impedance. At zero temperature, zero-point quantum fluctuations lead to a strong suppression of the persistent current with decreasing external impedance. We emphasize the role of displacement currents in the dynamical fluctuations of the persistent current and show that with decreasing external impedance the fluctuations exceed the average persistent current.     

Entropy production and time asymmetry in nonequilibrium fluctuations

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems: namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant.     

Chaotic transition of random dynamical systems and chaos synchronization by common noises

We studied the mechanism behind the connection between the transition to chaos of random dynamical systems and the synchronization of chaotic maps driven by external common noises. Near the chaotic transition, the spatial size of random dynamical systems shows an extreme intermittent behavior. By calculating the scaling exponents, we have found that the origin of this intermittent behavior is on-off intermittency. This led us to conclude that chaotic transitions through on-off intermittency can be regarded as a route for random dynamical systems. To clarify this argument, a two-dimensional random dynamical system and two coupled logistic maps driven by external common noises were analyzed.     

Dynamical critical slowing down in CsNiF3

Dynamical critical slowing down in CsNiF₃ is studied using the a.c. susceptibility measurements at 9.5 GHz in zero external static magnetic field. The dynamical critical exponent for the relaxation time of the in-plane spin fluctuations is obtained for the temperature interval 6 K < T < 20 K. For this temperature interval where one-dimensional spin fluctuations are dominant, very good qualitative and quantitative agreement with the spinwave calculation of the dynamical response is obtained at long wavelength and low frequency. The dynamical critical exponent for the relaxation time is measured to be 0.96 ± 0.6. At higher temperature, a gradual crossover to an isotropic Heisenberg chain behaviour is observed. For temperatures close to the 3-d antiferromagnetic ordering temperature T_N, a crossover to 3-d fluctuation regime gives rise to a speeding-up of the spin relaxation rate.     

Fixed past and uncertain future: A single-time covariant quantum particle mechanics

A covariant quantum mechanics for systems of finite-mass particles at finite energy follows from interpreting as Wick-Yukawa fluctuations in particle number the quantum fluctuations which are needed by Phipps to understand measurement theory and by Gyftopoulos to understand the second law of thermodynamics. The dynamical one-variable equations require as input the (N ? 1)-particle transition matrices and an N-N vertex or coupling constants at three-particle vertices.     

Implications of Noise on Neural Correlates of Consciousness: A Computational Analysis of Stochastic Systems of Mutually Connected Processes

Random fluctuations in neuronal processes may contribute to variability in perception and increase the information capacity of neuronal networks. Various sources of random processes have been characterized in the nervous system on different levels. However, in the context of neural correlates of consciousness, the robustness of mechanisms of conscious perception against inherent noise in neural dynamical systems is poorly understood. In this paper, a stochastic model is developed to study the implications of noise on dynamical systems that mimic neural correlates of consciousness. We computed power spectral densities and spectral entropy values for dynamical systems that contain a number of mutually connected processes. Interestingly, we found that spectral entropy decreases linearly as the number of processes within the system doubles. Further, power spectral density frequencies shift to higher values as system size increases, revealing an increasing impact of negative feedback loops and regulations on the dynamics of larger systems. Overall, our stochastic modeling and analysis results reveal that large dynamical systems of mutually connected and negatively regulated processes are more robust against inherent noise than small systems.     

Bifurcations and chaos in a semiconductor laser with coherent or noisy optical injection

This paper investigates theoretically the dynamical sensitivity of semiconductor lasers to external optical signals. Bifurcation analysis of ordinary rate equations, describing noise-free lasers with pure coherent external signal, reveals that considerable modifications to the extend and type of externally induced bifurcations and chaos are possible by tailoring of the laser active-medium and resonator configurations. Extending the analysis to stochastic rate equations, which describe lasers with spontaneous emission noise and noisy external signal, reveals further dynamical effects owing to the introduced random fluctuations. In particular, phase-fluctuations (incoherence) in the external signal can have a dramatic impact on induced bifurcations and chaos. The observed strong sensitivity of laser instabilities to the intensity and coherence of external signal can provide a very sensitive means to detect ultra low levels of laser radiation.     

Reconstruction of complex dynamical systems affected by strong measurement noise

This Letter reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as well as dynamical noise which is an intrinsic part of the dynamical process can be quantified correctly, solely on the basis of measured time series and proper data analysis. Finally, real world data sets are presented pointing out the relevance of the new approach.     

Diffusion dynamics in external noise-activated non-equilibrium open system-reservoir coupling environment

The diffusion process in an external noise-activated non-equilibrium open system-reservoir coupling environment is studied by analytically solving the generalized Langevin equation. The dynamical property of the system near the barrier top is investigated in detail by numerically calculating the quantities such as mean diffusion path, invariance, barrier passing probability, and so on. It is found that, comparing with the unfavorable effect of internal fluctuations, the external noise activation is sometimes beneficial to the diffusion process. An optimal strength of external activation or correlation time of the internal fluctuation is expected for the diffusing particle to have a maximal probability to escape from the potential well.     

Effects of randomness on chaos and order of coupled logistic maps

Natural systems are essentially nonlinear being neither completely ordered nor completely random. These nonlinearities are responsible for a great variety of possibilities that includes chaos. On this basis, the effect of randomness on chaos and order of nonlinear dynamical systems is an important feature to be understood. This Letter considers randomness as fluctuations and uncertainties due to noise and investigates its influence in the nonlinear dynamical behavior of coupled logistic maps. The noise effect is included by adding random variations either to parameters or to state variables. Besides, the coupling uncertainty is investigated by assuming tinny values for the connection parameters, representing the idea that all Nature is, in some sense, weakly connected. Results from numerical simulations show situations where noise alters the system nonlinear dynamics.     

Supernarrow spectral peaks near a kinetic phase transition in a driven nonlinear micromechanical oscillator

We measure the spectral densities of fluctuations of an underdamped nonlinear micromechanical oscillator. By applying a sufficiently large periodic excitation, two stable dynamical states are obtained within a particular range of driving frequency. White noise is injected into the excitation, allowing the system to overcome the activation barrier and switch between the two states. While the oscillator predominately resides in one of the two states for most frequencies, a narrow range of frequencies exist where the occupations of the two states are approximately equal. At these frequencies, the oscillator undergoes a kinetic phase transition that resembles the phase transition of thermal equilibrium systems. We observe a supernarrow peak in the spectral densities of fluctuations of the oscillator. This peak is centered at the excitation frequency and arises as a result of noise-induced transitions between the two dynamical states.     

Stochastic resonance mechanism in aerosol index dynamics

We consider satellite time series concerning the atmospheric aerosol content. We prove that these time series are well described by a stochastic dynamical model. The principal peak in the power spectrum of these signals can be explained by stochastic resonance, linking variable external factors, such as Sun-Earth radiation budget and local insolation, to fluctuations on smaller spatial and temporal scale due to internal weather and antrophic components.     

Dynamic control and information processing in chemical reaction systems by tuning self-organization behavior

Specific external control of chemical reaction systems and both dynamic control and signal processing as central functions in biochemical reaction systems are important issues of modern nonlinear science. For example nonlinear input-output behavior and its regulation are crucial for the maintainance of the life process that requires extensive communication between cells and their environment. An important question is how the dynamical behavior of biochemical systems is controlled and how they process information transmitted by incoming signals. But also from a general point of view external forcing of complex chemical reaction processes is important in many application areas ranging from chemical engineering to biomedicine. In order to study such control issues numerically, here, we choose a well characterized chemical system, the CO oxidation on Pt(110), which is interesting per se as an externally forced chemical oscillator model. We show numerically that tuning of temporal self-organization by input signals in this simple nonlinear chemical reaction exhibiting oscillatory behavior can in principle be exploited for both specific external control of dynamical system behavior and processing of complex information.     

Critical fluctuations of noisy period-doubling maps

We extend the theory of quasipotentials in dynamical systems by calculating, within a broad class of period-doubling maps, an exact potential for the critical fluctuations of pitchfork bifurcations in the weak noise limit. These far-from-equilibrium fluctuations are described by finite-size mean field theory, placing their static properties in the same universality class as the Ising model on a complete graph. We demonstrate that the effective system size of noisy period-doubling bifurcations exhibits universal scaling behavior along period-doubling routes to chaos.