Experimental evidence of coherence resonance in an optical system

Experimental evidence of coherence resonance in an optical system is reported. We show that the regularity of the excitable pulses in the intensity of a laser diode with optical feedback increases when adding noise, up to an optimal value of the noise strength. Both phase and amplitude fluctuations of the pulses play a relevant role in the dynamics of the system. We introduce the joint entropy of the two variables to generalize the indicator of coherence, and we put in evidence the mechanism of destruction of the excitable orbit after the resonance.     

随机扰动对螺旋波动力学的影响研究

心脏中的心肌组织是一种典型的可激发介质, 鉴于心肌细胞分布的离散性, 采用离散可激发介质模型研究了不应态时间随机扰动对螺旋波动力学行为的影响, 在扰动随机出现情况下, 螺旋波的稳定性与受扰元胞的数目和扰动幅度有关, 数值计算结果表明: 在适当的条件下, 可以观察到螺旋波漫游、破碎和消失现象, 并简要分析了产生这些现象的机理. 关键词： 螺旋波 激发介质 随机扰动     

Oscillatory traveling waves in excitable media

A new type of waves in an excitable medium, characterized by oscillatory profile, is described. The excitable medium is modeled by a two-component activator-inhibitor system. Reaction-diffusion systems with diagonal and cross diffusion are examined. As an example, a front (kink) represented by a heteroclinic orbit in the phase space is considered. The wave shape and velocity are analyzed with the use of exact analytical solutions for wave profiles.     

两层耦合可激发介质中螺旋波转变为平面波

采用Br-Eiswirth模型研究了两层耦合可激发介质中螺旋波的动力学,两层介质通过网络连接,即在每一层介质上,每一列选一个可激发单元作为中心点,在一层介质上同一列的可激发单元只与另一层介质上对应的中心点及其8个邻居有耦合.数值模拟结果表明:通过这种局部耦合,在适当小的耦合强度下两耦合螺旋波可实现同步,增大耦合强度会导致螺旋波漫游和漂移,造成螺旋波不同步,观察到螺旋波与静息态、低频平面波和不规则斑图共存现象.在适当强的耦合强度下,还观察到两螺旋波转变成同步的平面波消失现象.对产生这些现象的物理机理做了讨论.     

Excitability mediated by localized structures in a dissipative nonlinear optical cavity

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point there is a regime of excitable localized structures under the application of suitable perturbations. Excitability emerges from the spatial dependence since the system does not exhibit any excitable behavior locally. We show that the whole scenario is organized by a Takens-Bogdanov codimension-2 bifurcation point.     

Using weak impulses to suppress traveling waves in excitable media

Here we propose mechanisms for suppressing non-steady-state motions--propagating pulses, spiral waves, spiral-wave chaos--in excitable media. Our approach is based on two points: (1) excitable media are multistable; and (2) traveling waves in excitable media can be separated into fast and slow motions, which can be considered independently. We show that weak impulses can be used to change the values of the slow variable at the front and back of a traveling wave, which leads to wave front and wave back velocities that are different from each other. This effect can destabilize the traveling wave, resulting in a transition to the rest state.     

Simulations of a graphene excitable laser for spike processing

We propose and simulate a novel excitable laser employing passively \(Q\) -switching with a graphene saturable absorber for spike processing. Our approach combines the picosecond processing and switching capabilities of both linear and nonlinear optical device technologies to integrate both analog and digital optical processing into a single hardware architecture capable of computation without the need for analog-to-digital conversion. We simulate the laser using the Yamada model—a three-dimensional dynamical system of rate equations—and show behavior that is typical of spiking processing algorithms simulated in small circuits of excitable lasers.     

Covariant stringlike dynamics of scroll wave filaments in anisotropic cardiac tissue

It has been hypothesized that stationary scroll wave filaments in cardiac tissue describe a geodesic in a curved space whose metric is the inverse diffusion tensor. Several numerical studies support this hypothesis, but no analytical proof has been provided yet for general anisotropy. In this Letter, we derive dynamic equations for the filament in the case of general anisotropy. These equations are covariant under general spatial coordinate transformations and describe the motion of a stringlike object in a curved space whose metric tensor is the inverse diffusion tensor. Therefore the behavior of scroll wave filaments in excitable media with anisotropy is similar to the one of cosmic strings in a curved universe. Our dynamic equations are valid for thin filaments and for general anisotropy. We show that stationary filaments obey the geodesic equation.     

Mutual spatiotemporal coherence of optical fields in an amplitude-splitting interferometer

We have considered cross correlations of wave perturbations formed by optical fields at different points of space at the exit of an interferometer with the splitting of the amplitude of the initial wave field. Expressions for the longitudinal spatiotemporal cross-correlation function of perturbations on the optical axis of a Michelson interferometer have been obtained and analyzed. We have determined spatial and temporal intervals in which the wave fields excite mutually coherent perturbations in the exit channel of the interferometer in the free space and in the image space of the lens system. We have found that, in the free space, mutually correlated perturbations arise simultaneously in identical longitudinal intervals, whereas, in the image space, they arise at different times in spatial and temporal intervals varying along the optical axis of the lens. The influence of cross correlations of the wave fields on the interferometer signal has been analyzed.

     

Noise-induced spatial dynamics in the presence of memory loss

We study the spatial dynamics of noise-induced waves in two-dimensional excitable media in dependence on the duration of the artificially imposed refractory time that is introduced to each constitutive system unit after an excitation. Due to the introduction of refractory times, a randomly induced spatial wave is temporarily unable to transmit information to the opposite site of its propagation direction. Thus, once the wave leaves the absorbing boundaries of the spatial grid the system has little or no recollection, depending on the duration of the refractory time, of its existence. We show that even in the presence of such memory loss, self-organization of excitatory events leads to noise-induced spatial periodicity in the media. We present a simple analytical treatment of a two-unit system to capture and explain the essence of the observed phenomenon. Since refractory times are widespread in biological systems, our results provide interesting insights into functioning of real-life organisms at the cellular as well as tissue level.     

Fast thermo-optical excitability in a two-dimensional photonic crystal

We experimentally demonstrate excitability in a semiconductor two-dimensional photonic crystal. Excitability is a nonlinear dynamical mechanism underlying pulselike responses to small perturbations in systems possessing one stable state. We show that a band-edge photonic crystal resonator exhibits class II excitability, resulting from the nonlinear coupling between the high-Q optical mode, the charge-carrier density, and the fast (sub-micros) thermal dynamics. In this context, the critical slowing down of the electro-optical dynamics close to the excitable threshold can delay the optical response by an amount comparable to the duration of the output pulse (5 ns). The latter results from a short thermal dynamical excursion along a high local intensity manifold of the phase space.     

可激发介质中环形异质介质导致自维持靶波

在二维可激发介质中引入环形异质可激发介质,研究了可激发介质中自维持靶波的形成,数值模拟结果表明:当介质的激发性和环的尺寸适当选取时,初始的扰动可在可激发介质中产生自维持靶波,对产生自维持靶波的物理机理作了讨论.     

Excitability in a semiconductor laser with saturable absorber

We show that a monolithic and compact vertical cavity laser with intracavity saturable absorber can emit short excitable pulses. These calibrated optical pulses can be excited as a response to an input perturbation whose amplitude is above a certain threshold. Subnanosecond excitable response is promising for applications to novel all-optical devices for information processing or logical gates.     

Negative filament tension in the Luo-Rudy model of cardiac tissue

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, which lethality is widely known. One of the possible mechanisms of scroll wave instability is negative filament tension, which was studied theoretically using low-dimensional models of excitable medium. In this article we perform a numerical study of negative filament tension using the Luo-Rudy phase 1 model, which is widely used in cardiac electrophysiology. We show that this instability exists in this model, study its manifestation and discuss its relation to cardiac arrhythmogenesis.     

Lattice Boltzmann simulation for the energy and entropy of excitable systems

The internal energy and the spatiotemporal entropy of excitable systems are investigated with the lattice Boltzmann method.The numerical results show that the breakup of spiral wave is attributed to the inadequate supply of energy,i.e.,the internal energy of system is smaller than the energy of self-sustained spiral wave.It is observed that the average internal energy of a regular wave state reduces with its spatiotemporal entropy decreasing.Interestingly,although the energy difference between two regular wave states is very small,the different states can be distinguished obviously due to the large difference between their spatiotemporal entropies.In addition,when the unstable spiral wave converts into the spatiotemporal chaos,the internal energy of system decreases,while the spatiotemporal entropy increases,which behaves as the thermodynamic entropy in an isolated system.     

局部激励法产生靶波来消除螺旋波

提出采用局部激励方法产生靶波来消除抑制激发介质中的漂移(和稳定的)螺旋波．通过在系统中任意选择一个格点进行采样，将采样格点信号反馈到系统局部区域可产生一个稳定的靶波．数值计算表明：该方法可以消除均匀和非均匀介质(扩散系数随时间或空间变化)中的螺旋波(稳定旋转的螺旋波和漂移的螺旋波)，并且对于时空噪声具有一定的抗干扰性．     

Wave propagation in an excitable medium with a negatively sloped restitution curve

Recent experimental studies show that the restitution curve of cardiac tissue can have a negative slope. We study how the negative slope of the restitution curve can influence basic processes in excitable media, such as periodic forcing of an excitable cell, circulation of a pulse in a ring, and spiral wave rotation in two dimensions. We show that negatively sloped restitution curve can result in instabilities if the slope of the restitution curve is steeper than -1 and report different manifestations of this instability. (c) 2002 American Institute of Physics.     

Mechanism for spiral wave breakup in excitable and oscillatory media

We study spiral wave breakup using a Fitzhugh-Nagumo-type system. We find that spiral wave breakup can occur near the core or far from it in both excitable and oscillatory regimes. There is a faraway breakup scenario in both excitable and oscillatory media that depends on long wavelength modulation modes. We observed three distinct scenarios, including one that involves breakup that does not develop into turbulence. However, we find that the mechanisms behind these three scenarios are the same: they are caused by the interaction between the dispersion relation and the asymptotic behavior of the modulation mode. The difference in phenomenology is due to the asymptotic behavior of the modulation mode.     

Solitary waves, steepening and initial collapse in the Maxwell–Lorentz system

We present a numerical study of Maxwell’s equations in nonlinear dispersive optical media describing propagation of pulses in one Cartesian space dimension. Dispersion and nonlinearity are accounted for by a linear Lorentz model and an instantaneous Kerr nonlinearity, respectively. The dispersion relation reveals various asymptotic regimes such as Schrödinger and KdV branches. Existence of soliton-type solutions in the Schrödinger regime and light bullets containing few optical cycles together with dark solitons are illustrated numerically. Envelope collapse regimes of the Schrödinger equation are compared to the full system and an arrest mechanism is clearly identified when the spectral width of the initial pulse broadens beyond the applicability of the asymptotic behavior. We show that beyond a certain threshold the carrier wave steepens into an infinite gradient similarly to the canonical Majda–Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities.