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Results for “bistability”

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At least 811 records · Page 45Linked to original sources
PubMed1999

Synchronization of noisy systems by stochastic signals.

We study, in terms of synchronization, the nonlinear response of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level-this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train.

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PubMed2000

Noise sustained propagation: local versus global noise

We expand on prior results on noise supported signal propagation in arrays of coupled bistable elements. We present and compare experimental and numerical results for kink propagation under the influence of local and global fluctuations. As demonstrated previously for local noise, an optimum range of global noise power exists for which the medium acts as a reliable transmission "channel." We discuss implications for propagation failure in a model of cardiac tissue, and present a general theoretical framework based on discrete kink statistics. Valid for generic bistable chains, the theory captures the essential features observed in our experiments and numerical simulations.

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PubMed2000

Coherence and stochastic resonance in a two-state system

The subject of our study is a two-state dynamics driven by Gaussian white noise and a weak harmonic signal. The system resulting from a piecewise linear FizHugh-Nagumo model in the case of perfect time scale separation between fast and slow variables shows either bistable, excitable, or oscillatory behavior. Its output spectra as well as the spectral power amplification of the signal can be calculated for arbitrary noise strength and frequency, allowing characterization of the coherence resonance in the bistable and excitable regimes as well as quantification of nonadiabatic resonances with respect to the external signal in all regimes.

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PubMed2000

Phase dynamics of nearly stationary patterns in activator-inhibitor systems

The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The derivation applies to the bistable, excitable, and Turing unstable regimes. In the bistable case stability thresholds are obtained for the Eckhaus and zigzag instabilities and for the transition to traveling waves. Neutral stability curves demonstrate the destabilization of stationary planar patterns at low wave numbers to zigzag and traveling modes. Numerical solutions of the model system support the theoretical findings.

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PubMed2000

Domain segregation in a two-dimensional system in the presence of drift

Motivated by experiments on optical patterns we analyze two-dimensional extended bistable systems with drift after a quench above threshold. The evolution can be separated into successive stages: linear growth and diffusion, coarsening, and transport, leading finally to a quasi-one-dimensional kink-antikink state. The phenomenon is general and occurs when the bistability relates to uniform phases or two different patterns.

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PubMed2000

Compartmentalized reaction-diffusion systems.

Reaction-diffusion systems consisting of a collection of reactive domains separated by chemically inactive regions are considered. The reactive dynamics is governed by a multistep reaction mechanism and each reactive domain is specific to a particular elementary step or collection of elementary steps of the global reaction mechanism. Far-from-equilibrium situations where the global kinetics can give rise to complex states such as bistability or oscillations are studied. A general method for the calculation of the average concentration on each reactive domain is presented. The effects of compartmentalization are illustrated by a study of the influence of diffusion, reactive domain size, and domain distribution on the nature of the stationary states of the Schlögl model. Compartmentalization can drive the system into and out of the bistable regime of this reactive system.

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PubMed2001

Multifractal characterization of stochastic resonance.

We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force, singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence. We use also the proposed approach to characterize the noise-enhanced dynamics of a coupled stochastic neurons model.

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PubMed2001

Noninvasive control of stochastic resonance.

External feedback can enhance (or depress) the response of a noisy bistable system to monochromatic signals, significantly magnifying its natural stochastic resonance. We compare and contrast a variety of such feedback strategies, using both numerical simulations and analog electronic experiments. These noninvasive control techniques are especially valuable for noisy bistable systems that are difficult or impossible to modify internally.

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PubMed2001

Wave fronts and spatiotemporal chaos in an array of coupled Lorenz oscillators.

The effects of coupling strength and single-cell dynamics (SCD) on spatiotemporal pattern formation are studied in an array of Lorenz oscillators. Different spatiotemporal structures (stationary patterns, propagating wave fronts, short wavelength bifurcation) arise for bistable SCD, and two well differentiated types of spatiotemporal chaos for chaotic SCD (in correspondence with the transition from stationary patterns to propagating fronts). Wave-front propagation in the bistable regime is studied in terms of global bifurcation theory, while a short wavelength pattern region emerges through a pitchfork bifurcation.

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PubMed2001

Breathing current domains in globally coupled electrochemical systems: a comparison with a semiconductor model.

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional domain. The results are compared with the dynamics and the bifurcation scenarios occurring in a closely related model which describes pattern formation in semiconductors. Under galvanostatic control both systems are unstable with respect to the formation of stationary large amplitude current domains. The current domains as well as the homogeneous steady state exhibit oscillatory instabilities for slow dynamics of the potential drop across the double layer, or across the semiconductor device, respectively. The interplay of the different instabilities leads to complex spatio-temporal behavior. We find breathing current domains and chaotic spatio-temporal dynamics in the electrochemical system. Comparing these findings with the results obtained earlier for the semiconductor system, we outline bifurcation scenarios leading to complex dynamics in globally coupled bistable systems with subcritical spatial bifurcations.

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PubMed2001

Catalytic CO oxidation on nanoscale Pt facets: effect of interfacet CO diffusion on bifurcation and fluctuation behavior.

We present lattice-gas modeling of the steady-state behavior in CO oxidation on the facets of nanoscale metal clusters, with coupling via interfacet CO diffusion. The model incorporates the key aspects of the reaction process, such as rapid CO mobility within each facet and strong nearest-neighbor repulsion between adsorbed O. The former justifies our use of a "hybrid" simulation approach treating the CO coverage as a mean-field parameter. For an isolated facet, there is one bistable region where the system can exist in either a reactive state (with high oxygen coverage) or a (nearly CO-poisoned) inactive state. Diffusion between two facets is shown to induce complex multistability in the steady states of the system. The bifurcation diagram exhibits two regions with bistabilities due to the difference between adsorption properties of the facets. We explore the role of enhanced fluctuations in the proximity of a cusp bifurcation point associated with one facet in producing transitions between stable states on that facet, as well as their influence on fluctuations on the other facet. The results are expected to shed more light on the reaction kinetics for supported catalysts.

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PubMed2002

Stochastic resonance for motion of flexible macromolecules in solution.

We consider a dilute or semidilute polymer solution with localized attracting centers near a flat phase boundary and assume it driven by both stochastic and periodic forces. The attracting inhomogeneities restrict the free motion of macromolecules and play the role of fixed pinning centers. The flat boundary is modeled by a bistable potential whose minima attract the movable polymer segments between neighboring pinning points. We study the motion of these segments. The stochastic forces lead to stochastic oscillations of the polymer parts between the two potential wells near the phase boundary. Application of a small temporal periodic force can synchronize these oscillations and leads to the phenomenon of stochastic resonance for a nonvanishing noise intensity. As an outcome of our theory in agreement with numerical simulations, the resonance is stronger for wider and/or less deep potentials and observed at smaller values of the noise intensity. Additionally, we discuss under what conditions doubly stochastic resonance of the macromolecular motion occurs, that is, if bistability of the potential near the boundary originates in the action of multiplicative noise.

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PubMed2002

Dynamical effects induced by long range activation in a nonequilibrium reaction-diffusion system.

We show both experimentally and numerically that the time scales separation introduced by long range activation can induce oscillations and excitability in nonequilibrium reaction-diffusion systems that would otherwise only exhibit bistability. Namely, we show that in the chlorite-tetrathionate reaction, where the autocatalytic species H+ diffuses faster than the substrates, the spatial bistability domain in the nonequilibrium phase diagram is extended with oscillatory and excitability domains. A simple model and a more realistic model qualitatively account for the observed dynamical behavior. The latter model provides quantitative agreement with the experiments.

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PubMed2003

Asymptotic solutions of stationary patterns in convection-reaction-diffusion systems.

We study and map the possible stationary patterns that emerge in a convection-reaction-diffusion (CRD) system using a learning polynomial kinetics. We classify the patterns according to the kinetic model (oscillatory, bistable, or intermediate), the instability nature of the bounded system (convective or absolute), the applied boundary conditions and the system length. This analysis presents a unifying approach to various pattern-inducing mechanisms such as DIFICI (differential flow induced chemical instability), which predicts moving patterns in systems with wide difference of convective rates, and differential capacity patterns, which predicts stationary patterns in cross-flow reactors with a large heat capacity. Previous studies of CRD systems have considered only oscillatory kinetics. Nonlinear analysis, which follows the front motion by approximating its velocity, accounts for the stability of the stationary, whether spatially periodic or other, patterns. The most dominant state is the large-amplitude stationary spatially periodic pattern. With oscillatory kinetics these emerge in the convectively unstable domain above the amplification threshold. The domain of absolute instability, which is determined analytically for unbounded systems, is divided in the bounded system into two subdomains with moving DIFICI waves or stationary patterns. With bistable kinetics the large-amplitude stationary patterns can be sustained only within a narrow subdomain but other stationary patterns, that incorporate several fronts upstream and an "almost homogeneous" tail downstream, can be sustained as well. With intermediate kinetics the large-amplitude axisymmetric stationary patterns may coexist with small-amplitude stationary nonaxisymmetric patterns.

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PubMed2003

Effect of spontaneous polarization and polar surface anchoring on the director and layer structure in surface-stabilized ferroelectric liquid crystal cells.

We use the Landau-de Gennes model to study theoretically the effect of the magnitude of the spontaneous polarization (P(S)), the ratio (r) between the equilibrium layer tilt and the smectic cone angle, the thickness of the insulating alignment layers and the strength of the polar and nonpolar surface anchoring on the director and layer structure in surface-stabilized ferroelectric liquid crystal cells with the chevron structure of smectic layers. The system shows a surprising number of stable structures, accompanied by one or two metastable ones. At P(S) greater than the critical value only quasimonostable structures, which can exhibit the thresholdless (V-shaped) switching, exist at all r and both at weak and strong polar surface anchoring. At lower P(S) bistable and monostable structures can coexist. Bistable structures can be expected at high r, low P(S) and if polar surface anchoring is weaker than the nonpolar one. Lowering the ratio r and/or increasing the strength of polar anchoring promotes the stability of monostable structures. Thicker insulating alignment layers also drive the system into the monostable state. Polar surface anchoring induces a large surface electroclinic effect. As a result the nematic deformations close to the surfaces are very strong and the stress is relieved by bending of the smectic layers. This leads to the formation of a double chevron structure which is stable at very large polar anchoring and due to the surface electroclinic effect it is metastable also at lower values of polar anchoring.

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PubMed2004

Unidirectional drift of fronts under zero-mean force, and broken symmetries of the rate function.

The deterministic front-ratchet effect, namely, the unidirectional transport of the bistable fronts (BFs) under the additive zero-mean ac forcing, is considered within the piecewise-linear model of the bistable system. Two different mechanisms underlying the front ratchet, two cases of the broken symmetry of (i) the rate function, and/or (ii) the external zero-mean ac forcing are analyzed. Types of unidirectional motion, some versions of the "unforced" migration of BFs, are found in both cases of the travelling (initially propagating) and the static (motionless) fronts. We show that symmetry breaking in the front ratchet could produce progressive, regressive, and reversal types of the unidirectional motion of traveling BFs. By tuning the parameters of the rate function the propagation direction of BF exhibits reversal, as a function of the amplitude of the applied ac forcing. The static BFs, which stay initially at rest, can gain the dc motion discussed if the symmetry of either the rate function or the applied ac forcing is broken. The adiabatic approximation is used. To perform a rigorous analytic treatment for the arbitrary strengths of the driving force we assume that the frequency of the applied ac forcing is small, if compared to the characteristic relaxation rates in the system.

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PubMed2004

Computer simulation of a liquid-crystal anchoring transition.

We present a study of the effects of confinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential. Using geometrical arguments to calculate the molecular volume absorbed at the substrates, we show that both planar and homeotropic arrangements can be obtained using this model. Monte Carlo simulations are then used to perform a systematic study of the model's behavior as a function of the system density and the hard-needle-wall interaction parameter. As well as showing the homeotropic to planar anchoring transition, the anchoring phase diagrams computed from these simulations indicate regions of bistability. This bistable behavior is examined further through the explicit simulation of field-induced two-way switching between the two arrangements.

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PubMed2004

Experimental and theoretical study of the noise-induced gain degradation in vibrational resonance.

We present the results of theoretical and experimental investigations of the effect of additive noise on vibrational resonance in a bistable system driven by two periodic forces with very different frequencies. The phenomenon shows up as a parametric amplification of the low-frequency signal depending on the amplitude of high-frequency modulation. A scaling law for noise-induced decreasing of the gain factor, found theoretically, is compared with the experimental results obtained in a bistable vertical cavity surface emitting laser.

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