Delay-enhanced coherence of spiral waves in noisy Hodgkin-Huxley neuronal networks

We study the spatial dynamics of spiral waves in noisy Hodgkin-Huxley neuronal ensembles evoked by different information transmission delays and network topologies. In classical settings of coherence resonance the intensity of noise is fine-tuned so as to optimize the system's response. Here, we keep the noise intensity constant, and instead, vary the length of information transmission delay amongst coupled neurons. We show that there exists an intermediate transmission delay by which the spiral waves are optimally ordered, hence indicating the existence of delay-enhanced coherence of spatial dynamics in the examined system. Additionally, we examine the robustness of this phenomenon as the diffusive interaction topology changes towards the small-world type, and discover that shortcut links amongst distant neurons hinder the emergence of coherent spiral waves irrespective of transmission delay length. Presented results thus provide insights that could facilitate the understanding of information transmission delay on realistic neuronal networks.     

Instability of photoexcited electron-hole plasma in short semiconductor structures

The instability of the electron-hole plasma produced by continuous photoexcitation in short semiconductor structures is investigated theoretically. The applied electric field is considerably disturbed by photogenerated charge carriers. At a sufficiently intensive photogeneration plasma instability occurs. The frequency of current oscillations due to the instability, as shown by numerical simulation for a GaAs structure, is in the range of 10¹¹–10¹²s^–1.     

Pacemaker-guided noise-induced spatial periodicity in excitable media

We study the impact of subthreshold periodic pacemaker activity and internal noise on the spatial dynamics of excitable media. For this purpose, we examine two systems that both consist of diffusively coupled units. In the first case, the local dynamics of the units is driven by a simple one-dimensional model of excitability with a piece-wise linear potential. In the second case, a more realistic biological system is studied, and the local dynamics is driven by a model for calcium oscillations. Internal noise is introduced via the τ-leap stochastic integration procedure and its intensity is determined by the finite size of each constitutive system unit. We show that there exists an intermediate level of internal stochasticity for which the localized pacemaker activity maps best into coherent periodic waves, whose spatial frequency is uniquely determined by the local subthreshold forcing. Via an analytical treatment of the simple minimal model for the excitable spatially extended system, we explicitly link the pacemaker activity with the spatial dynamics and determine necessary conditions that warrant the observation of the phenomenon in excitable media. Our results could prove useful for the understanding of interplay between local and global agonists affecting the functioning of tissue and organs.     

Correlated noise induced spatiotemporal coherence resonance in a square lattice network

The effects of additive correlated noise, which is composed of common Gaussian white noise and local Gaussian colored noise, on a square lattice network locally modelled by the Rulkov map are studied. We focus on the ability of noise to induce pattern formation in a resonant manner. It is shown that local Gaussian colored noise is able to induce pattern formation, which is more coherent at some noise intensity or correlation time, so it is able to induce spatiotemporal coherence resonance in the network. When common Gaussian white noise is applied in addition, it is seen that the correlated noise can induce coherent spatial structures at some intermediate noise correlation, while this is not the case for smaller and larger noise intensities. The mechanism of the observed spatiotemporal coherence resonance is discussed. It is also found that the correlation time of local colored noise has no evident effect on the optimal value of the noise strength for spatiotemporal coherence resonance in the network.     

Logarithmic frequency scaling of semiconductor oscillations caused by a modified saddle-node bifurcation on a limit cycle

The oscillatory behavior of low-temperature impact ionization breakdown inp-type germanium is investigated experimentally. We explain the anomalous scaling behavior of a saddle-node bifurcation on a limit cycle in terms of a simple model approach. It represents the low-dimensional analog to a new type of intermittency proposed recently.     

Statistical appearance of nonuniform fluctuations in a wide-gap n-n-n-n device

A cross-correlation matrix applied for restoring the doping profile in an n⁺-n⁻-n-n⁺ device was reported recently [Y.-H. Shiau, Solid-State Electron. 50 (2006) 191]. In this paper we will show that this statistical method is very useful for detecting the dynamical processes embedded in semiconductor devices. In addition, extraction of nonuniform fluctuations hidden in this wide-gap semiconductor device could be helpful for clarifying the previous studies on several competing instabilities in InSb at 77 K [A. ?enys, G. Lasiene, K. Pyragas, Solid-State Electron. 35 (1992) 975; H. Ito, Y. Ueda, Phys. Lett. A 280 (2001) 312]. A general discussion about the application of the cross-correlation matrix to other pattern-forming systems is also given in the present study.     

Nonlinear response and chaos in semiconductors induced by impact ionization

A review is given of the nonlinear response and chaos induced by impact ionization of neutral shallow donors, observed in n-GaAs. Two kinds of the observation are described; (i) firing wave instability, and (ii) periodically driven current filament. For the firing wave instability, several important aspects are discussed including the selective excitation of the current filaments and the deterministic nature of the firing density wave. The nonlinear response of a periodically driven current filament has been investigated by applying a dc+ac bias of the form ofV _dc+V _ac sin(2f ₀ t), wheref ₀1 MHz. The carrier dynamics and the bifurcation routes to chaos are discussed in terms of the observed phase diagram and the bifurcation map. The deterministic nature of the strange attractors are described in detail in terms of the correlation dimension and the Kolmogorov entropy.     

Bifurcation phenomena in a periodically driven current filament and a conjecture on the turbulent patterns by computer simulations

Bifurcation routes to chaos in a periodically driven current filament have been studied by computer simulations. By an impact ionization model, theS-shaped currentvoltage curve is perturbed by the dc+ac bias ofE ₀+E _acsin(27f ₀t). The bifurcation maps are described as a function ofE ₀. In the prebreakdown region, the fractal basin boundary, the crisis and the intermittency are discussed, based on the general considerations of the carrier dynamics on the catastrophe manifold. The intermittent burst of the current filament is explained by the destabilization of the weak turbulence generated in the lower branch. In the diffusion-reaction model, the spatio-temporal mode patterns of the transverse carrier profile have revealed the competitive evolution of the hyper-freezing and the firing.     

Autoresonant excitation of multiphase waves in the sine-Gordon model

Autoresonant excitation and control of multiphase waves of the sine-Gordon equation is discussed. The autoresonance (a persistent nonlinear phase-locking) is achieved by applying chirped frequency wave-like perturbations and passage through resonances with inactive (dormant) degrees of freedom in the system. Successful phase locking requires the amplitude of the driving perturbation to exceed a threshold that scales as 3/4 power of the driving frequency chirp rate. The spectral theory of the inverse scattering transform method is used for diagnostics and analysis of the excited solutions.     

Complex Ginzburg-Landau equation for nonlinear travelling waves in extrinsic semiconductors

We study the nonlinear state of a travelling-wave instability occurring close to the onset of impact ionization in extrinsic semiconductors. Our investigations are based on a complex Ginzburg-Landau equation (CGLE). For a simple generation-recombination function including impact ionization and thermal recombination of the charge carriers, we find a supercritical bifurcation of stable travelling waves for most parameter values. The results are compared with a numerical solution of the basic equations of motion. Furthermore, we expect that weak turbulence phenomena should be observed in semiconductors if their specific generation-recombination kinetics leads to a CGLE with appropriate coefficients.     

Theoretical approaches to nonlinear and chaotic dynamics of generation-recombination processes in semiconductors

We present an overview of recent progress in the theoretical modelling of nonlinear and chaotic dynamics induced by generation and recombination processes of charge carriers. Impact ionisation of impurities is the autocatalytic, i.e. destabilizing, step of three different physical mechanisms for spontaneous, self-sustained oscillations of the carrier density. The restoring force is furnished by one of the following three processes: (i) dielectric relaxation of the internal electric field, (ii) energy relaxation of the hot carriers, and (iii) trapping at impurities, where the discrete nature of the individual generationrecombination processes is taken into account.     

Travel and tourism: Into a complex network

It is discussed how the worldwide tourist arrivals, about 10% of the world’s domestic product, form a largely heterogeneous and directed complex network. Remarkably the random network of connectivity is converted into a scale-free network of intensities. The importance of weights on network connections is brought into discussion. It is also shown how strategic positioning particularly benefits from market diversity and that interactions among countries prevail on a technological and economic pattern, questioning the backbone of driving forces in traveling.     

Structure of a financial cross-correlation matrix under attack

We investigate the structure of a perturbed stock market in terms of correlation matrices. For the purpose of perturbing a stock market, two distinct methods are used, namely local and global perturbation. The former involves replacing a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series while the latter reconstructs the cross-correlation matrix just after replacing the original return series with Gaussian-distributed time series. Concerning the local case, it is a technical study only and there is no attempt to model reality. The term ‘global’ means the overall effect of the replacement on other untouched returns. Through statistical analyses such as random matrix theory (RMT), network theory, and the correlation coefficient distributions, we show that the global structure of a stock market is vulnerable to perturbation. However, apart from in the analysis of inverse participation ratios (IPRs), the vulnerability becomes dull under a small-scale perturbation. This means that these analysis tools are inappropriate for monitoring the whole stock market due to the low sensitivity of a stock market to a small-scale perturbation. In contrast, when going down to the structure of business sectors, we confirm that correlation-based business sectors are regrouped in terms of IPRs. This result gives a clue about monitoring the effect of hidden intentions, which are revealed via portfolios taken mostly by large investors.     

Turbulence in a gas laser

We test a recent assertion [A. Muriel, Physica A 388 (4) (2009) 311] that a gas consisting of excited molecules is turbulent, in contrast to the laminar state of a gas of ground state molecules. Since a lasing gas is made up of excited molecules, we examine if a lasing gas system is indeed turbulent. Surprisingly, from a literature search, it appears that turbulence in a lasing gas medium has never been addressed. To test for turbulence, we use a recently proposed criterion for the existence of turbulence, the presence of multivalued steady-state velocity fields [P. Getreur, A. Albano, A. Muriel, Phys. Lett. A 366 (2007) 101]. To study this subject, we improve an old model of a gas of two-level atoms in a one-dimensional model [A. Muriel, M. Dresden, Physica D 94 (1996) 103] by including the effect of a radiation field with the use of Einstein A and B coefficients. A set of coupled equations for the velocity fields in one dimension are derived. The zeroth order implementation of an iterative solution establishes that the steady-state velocity fields are multivalued, given by the Lambert function. We obtain signature characteristics of turbulence such as velocity reversals, infinite gradients, and stagnation points.     

Geographical Effects on Complex Networks

We investigate how the geographical structure of a complex network affects its network topology, synchronization and the average spatial length of edges. The geographical structure means that the connecting probability of two nodes is related to the spatial distance of the two nodes. Our simulation results show that the geographical structure changes the network topology. The synchronization tendency is enhanced and the average spatial length of edges is enlarged when the node can randomly connect to the further one. Analytic results support our understanding of the phenomena.     

Differential System＇s Nonlinear Behaviour of Real Nonlinear Dynamical Systems

Chaos attractor behaviour is usually preserved if the four basic arithmetic operations, i.e. addition, subtraction, multiplication, division, or their compound, are applied. First-order differential systems of one-dimensional real discrete dynamical systems and nonautonomous real continuous-time dynamical systems are also dynamical systems and their Lyapunov exponents are kept, if they are twice differentiable. These two conclusions are shown here by the definitions of dynamical system and Lyapunov exponent. Numerical simulations support our analytical results. The conclusions can apply to higher order differential systems if their corresponding order differentials exist.     

Dynamical behaviors of inter-out-of-equilibrium state intervals in Korean futures exchange markets

A recently discovered feature of financial markets, the two-phase phenomenon, is utilized to categorize a financial time series into two phases, namely equilibrium and out-of-equilibrium states. For out-of-equilibrium states, we analyze the time intervals at which the state is revisited. The power-law distribution of inter-out-of-equilibrium state intervals is shown and we present an analogy with discrete-time heat bath dynamics, similar to random Ising systems. In the mean-field approximation, this model reduces to a one-dimensional multiplicative process. By varying global and local model parameters, the relevance between volatilities in financial markets and the interaction strengths between agents in the Ising model are investigated and discussed.     

Mapping between electronic structure and ac-Stark shift resonances in heterostructures

We have studied carrier dynamics in quantum wells subjected to strong ac-electric fields. The ac-Stark shifts were calculated within the Kane model. The inherent symmetries and couplings in Kane Hamiltonian lead to the carrier effective masses depending on the -vector. We have predicted a mapping between energy dispersion and ac-Stark effect. An anomalous behavior of light-hole states can be associated to the different dynamical responses of carrier to the driving ac-field.     

Spiking in an activator-inhibitor model for elements with S-shaped negative differential conductivity

Self-organized spatio-temporal dynamics of electrical transport is described by a simple noncubic activator-inhibitor system derived for layered semiconductor structures. The model exhibits a novel mode of self-sustained oscillations due to current filaments switching on and off (spiking) which may be periodic or chaotic. Additionally, we obtain complex multifilamentary spatio-temporal patterns. As such phenomena have been observed in various devices exhibiting S-shaped negative differential conductivity, our model is suggested to describe a generic mechanism.     

Frequency Sensitivity of Signal Detection in Scale-Free Networks

It has been recently reported that scale-free topology favors the detection of a weak signal because of the higher amplification at the hub node than that at other nodes [Phys. Ref. I？, 78（2008）046111]. We investigate the corresponding synchronization behaviors and find that the favorite detection depends not only on the coupling and noise strengths but also on the frequency of the external signal. We reveal theoretically and numerically that the amplification effect of the hub node will decrease monotonously with the external frequency, which is useful to understand the high sensitivity of animal visual and auditory systems to weak external signals.