Average Laminar Length Research Articles

Numerical study of type-I intermittency in an atmospheric-pressure dielectric barrier discharge

Atmospheric-pressure dielectric barrier discharge (AP-DBD) as a complex dissipative dynamical system exhibits rich temporal nonlinear and chaotic behavior. The intermittent chaos in AP-DBD, where the abrupt intensive currents break the regular periodic current oscillations during a discharge process, is studied by numerical simulation. By increasing the control parameter of applied voltage amplitude, random intensive currents occur more frequently, reducing the average laminar length (time interval of regular oscillations). It is found that the average laminar length depending on the control parameter follows the scaling law with an exponent of −0.5, implying a type-I intermittent discharge. This study further supplements and strengthens the nonlinear theory in plasma discharge.

Type-V intermittency from Markov binary block visibility graph perspective

In this work, type-V intermittency is studied from Markov binary block visibility graphs perspective. We considered a piecewise quadratic Poincare map that is a simple model to exhibit this type of intermittency. The mechanism of type-V intermittency is collision of a stable fixed point with a point of discontinuity of the Poincare map. We study the behavior of a dynamical system in the vicinity of the discontinuous or non-differentiable points (NDP) using networks language. Numerical results showed that there is a logarithmic scaling law logε for the average laminar length of the type-V intermittency. We also described their properties based on statistical tools such as the length between reinjection points and the average laminar length. For further investigation, we verified the degree distribution of the complex network generated by type-V intermittency time series and finally, predicted the behavior of type-V intermittency by the proposed theoretical degree distributions.

Transition to Frozen Antiferromagnetic Pattern in Delayed Logistic Map

We study nonlinearly coupled logistic map with feedback in the limit of large delay time ([Formula: see text]). In the [Formula: see text]’s, the mapping of delayed dynamical systems to the spatially extended system was pursued in the context of optical systems by Arecchi and coworkers. We map the delayed system to a coupled map lattice of size [Formula: see text] with a sequential update and strictly one-sided coupling. Apart from aiding visualization, this formal equivalence helps us identify “phases” in a delayed system. One of the easily identified phases is that of frozen antiferromagnetic phase which is abundant in phase space. As coupling parameter ([Formula: see text]) increases, the system goes from periodic cascades along the coarse-grain region to chaos. We use the number of domain walls as an order parameter for locating this transition. The domain walls undergo random walk with drift and annihilate each other. At critical parameter value, we observe the power-law decay of this parameter. The decay exponents fall within the directed Ising universality class in general. We also find the escape time distribution, i.e. time required for reaching frozen antiferromagnetic regime. It diverges as it approaches the critical point. The divergence of average laminar length shows features indicating crisis induced intermittency.

Noise effect on statistical properties of type-I intermittency

In this work we analyze the noise effect on type-I intermittency, for which we develop a methodology based on a recently proposed technique used to model the reinjection probability density (RPD). This new methodology allows us to study the noise effect on the intermittency statistical properties for relatively large noise strengths in a quadratic map with different reinjection mechanisms. We show that this procedure allows to predict the behavior of the noisy and noiseless system using the results of the M(x) function which is implemented to obtain the RPD function. We also derive an analytical approximation for the probability density of the laminar lengths and we obtain results for the average laminar length. All analytical approaches show a good agreement with the numerical results even though the statistical properties are calculated using either the noisy or noiseless data, however in some cases the description of the noiseless system using the noisy data can be inaccurate. In addition, we show that occasionally the presence of noise could be not detected due to the results behave as they would be corresponding to a noiseless system. This aspect may have important consequences especially when working with experimental data.

Current reversal with type-I intermittency in deterministic inertia ratchets.

The intermittency is investigated when the current reversal occurs in a deterministic inertia ratchet system. To determine which type the intermittency belongs to, we obtain the return map of velocities of particle by using stroboscopic recordings, and by numerically calculating the distribution of the average laminar length <l>. The distribution follows the scaling law of <l> proportional to epsilon(-1/2), the characteristic relation of type-I intermittency.

Experimental observation of characteristic relations of type-III intermittency in the presence of noise in a simple electronic circuit.

We investigate the characteristic relations of type-II and -III intermittencies in the presence of noise. The theoretically predicted characteristic relation is that <l> approximately exp[/epsilon/(2)] for a negative regime of epsilon and <l> approximately epsilon(-nu) for the positive regime of epsilon (1/2</=nu<1), where <l> is the average laminar length and (1+epsilon) is the slope of the local Poincaré map around the tangent point. We experimentally confirm these relations in a simple electronic circuit.

Universal scaling properties of type-I intermittent chaos in isolated resistance arteries are unaffected by endogenous nitric oxide synthesis

Spontaneous fluctuations in flow in isolated rabbit ear resistance arteries may exhibit almost-periodic behavior interrupted by chaotic bursts that can be classified as type-I Pomeau-Manneville intermittency. This conclusion was supported by the construction of parabolic return maps and identification of the characteristic probability distributions for the number of oscillations per laminar segment (n) associated with the type-I scenario. Pharmacological inhibition of nitric oxide (NO) synthesis by the vascular endothelium modulated the dynamics of the reinjection mechanism, and thus the generic shape of the probability distribution for n. Nevertheless, average laminar length was related to a derived bifurcation parameter epsilon according to power-law scaling of the form <n> approximately epsilon(beta), where the estimated critical exponent beta was close to the theoretical value of -0.5 both in the presence and absence of NO synthesis.

Intermittency in random maps

The escape probability for a random walk on a one-dimensional lattice is discussed in terms of random maps. The global dynamics is found to be intermittent: the laminar regions with long sojourn near the upper fixed point are broken by irregular bursts. Intermittency emerges even if the Sinai condition is not satisfied. It is shown that, if P is the probability of choosing the upper map, the average laminar length diverges as (1− P) − α .

Dynamics of the kicked logistic map

The modulation of the logistic map by a sequence of periodic kicks brings up a three-parameter kicked logistic map (klm) with new distinct dynamic features. Thus, its parameter space structure exhibits highly interleaved sets with different attractors, and complex basins of attraction are created. Additional roots to chaos and abrupt attractor changes are identified in the parameter space. The observed intermittency route to chaos is distinct to those typical of spatially discontinuous unidimensional maps, with a characteristic power-law dependence of the average laminar length on the control parameters. This behaviour is verified for both the internal and the transfer crisis-induced intermittency.

Influence of external noise in type V intermittency

The influence of external noise on type V intermittency has been studied both analytically and numerically based on a model map. The results show that there is a gradual divergence from the logarithmic dependence of the average laminar length on the control parameter and the hyperbolic secant distribution of laminar lengths when the strength of the external noise increases. That is in a good agreement with our experimental results obtained in an electronic relaxation oscillator.

New type of intermittency in discontinuous maps.

Intermittent behavior originating in a point of discontinuity in 1D maps is investigated. Studying the duration of the laminar phase, we find a logarithmic dependence of the average laminar length 〈l〉 on the control parameter \ensuremath{\epsilon}, in contrast to the three conventional types of intermittency characterized by power-law scaling. Analytical considerations give the relation 〈l〉=log(\ensuremath{\epsilon})/log(s)+\ensuremath{\beta} (where s is the ``slope'' at the point of discontinuity). Numerical data obtained from a relaxation oscillator model are in good agreement with these results.

Reconsideration of the renormalization-group theory on intermittent chaos

The renormalization-group theory has made us believe that the average laminar length for type III intermittency is inversely proportional to the control parameter. However this does not agree with the result of numerical computations. This contradiction is removed through studying the scaling relation for the length of each laminar.

Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator

For a driven nonlinear semiconductor oscillator which shows a period-doubling pitchfork bifurcation route to chaos, we report an additional route to chaos: the Pomeau-Manneville intermittency route, characterized by a periodic (laminar) phase interrupted by bursts of aperiodic behavior. This occurs near a tangent bifurcation as the system driving parameter is reduced by $\ensuremath{\epsilon}$ from the threshold value for a periodic window. Data are presented for the dependence of the average laminar length $〈l〉$ on $\ensuremath{\epsilon}$, and also on additive random noise voltage. The results are in reasonable agreement with the intermittency theory of Hirsch, Huberman, and Scalapino. The distribution $P(l)$ is also reported.