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Results for “stability boundary”

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PubMed2001

Stability in a metapopulation model with density-dependent dispersal.

A spatially explicit metapopulation model with positive density-dependent migration is analysed. We obtained conditions under which a previously stable system can be driven to instability caused by a density-dependent migration mechanism. The stability boundary depends on the rate of increase of the number of migrants on each site at local equilibrium, on the intrinsic rate of increase at local level, on the number of patches, and on topological aspects regarding the connectivity between patches. A concrete example is presented illustrating the dynamics on the dispersal-induced unstable regime.

Animals↗
PubMed1998

The evolution of diapause in a coupled host-parasitoid system.

Diapause of part of a population during a breeding opportunity is widespread among insects. We explore the evolution of such diapause in a coupled host-parasitoid system, using a discrete-generation population dynamic model that incorporates diapause. We show that diapause in the host tends to be a stabilizing factor while diapause in the parasitoid does not affect the stability boundaries. We then allow the frequency of diapause in the host and parasitoid to evolve, and find the joint population and evolutionary dynamic equilibrium by numerical methods. At the equilibrium, population dynamics exhibit cycles and host diapause always occurs. Parasitoid diapause often occurs, though this depends on exact parameter values. Thus, intrinsically generated fluctuations in fitness (due to cyclical population dynamics) lead to the evolution of diapause as a bet-hedging mechanism.

Animals↗
PubMed2001

Analysis of the reflexive feedback control loop during posture maintenance.

In previous work it has been shown in posture experiments of the human arm that reflexive dynamics were substantial for narrow-band stochastic force disturbances. The estimated reflex gains varied substantially with the frequency content of the disturbances. The present study analyses a simplified linear model of the reflexive feedback control loop, to provide an explanation for the observed behaviour. The model describes co-activation and reflexive feedback. The task instruction 'minimize the displacements' is represented mathematically by a cost function that is minimized by adjusting the parameters of the model. Small-amplitude displacements allow the system to be analysed with a quasilinear approach. The optimization results clarify the limited effectiveness of reflexive feedback on the system's closed-loop behaviour, which emanates from the time delay present in the reflex loops. For low-frequency inputs less than 5 Hz, boundary-stable solutions with high reflex gains are predicted to be optimal. Input frequencies near the system's eigenfrequency (about 5 Hz), however, would be amplified and result in oscillatory behaviour. As long as the disturbance does not excite these frequencies, boundary stability will be optimal. The predicted reflex gains show a striking similarity with the estimated reflex gains from the experimental study. The present model analysis also provides a clear explanation for the negative reflex gains, estimated for near-sinusoidal inputs beyond 1.5 Hz.

Feedback↗
PubMed1998

Analysis of an excitable dendritic spine with an activity-dependent stem conductance.

Dendritic spines are the major target for excitatory synaptic inputs in the vertebrate brain. They are tiny evaginations of the dendritic surface consisting of a bulbous head and a tenuous stem. Spines are considered to be an important locus for plastic changes underlying memory and learning processes. The findings that synaptic morphology may be activity-dependent and that spine head membrane may be endowed with voltage-dependent (excitable) channels is the motivation for this study. We first explore the dynamics, when an excitable, yet morphologically fixed spine receives a constant current input. Two parameter Andronov-Hopf bifurcation diagrams are constructed showing stability boundaries between oscillations and steady-states. We show how these boundaries can change as a function of both the spine stem conductance and the conductance load of the attached dendrite. Building on this reference case an idealized model for an activity-dependent spine is formulated and analyzed. Specifically we examine the possibility that the spine stem resistance, the tunable "synaptic weight" parameter identified by Rall and Rinzel, is activity-dependent. In the model the spine stem conductance depends (slowly) on the local electrical interactions between the spine head and the dendritic cable; parameter regimes are found for bursting, steady states, continuous spiking, and more complex oscillatory behavior. We find that conductance load of the dendrite strongly influences the burst pattern as well as other dynamics. When the spine head membrane potential exhibits relaxation oscillations a simple model is formulated that captures the dynamical features of the full model.

Dendrites↗
PubMed1983

A sectorial centrifuge cell for swinging bucket rotors--application to a velocity gradient centrifugation methodology.

A sectorial cell of 1.55 ml capacity, designed to be used in swinging bucket rotors, is introduced and applied to boundary sedimentation studies. The cell, made of polycarbonate by injection molding, represents an improvement over previously existing models in terms of resistance and attainable speeds. Its use has been extended to polydispersity determination by evaluation of the s value distribution function g(s) = dC/ds. The latter can be corrected to standard conditions (water at 20 degrees C), by using newly derived equations in connection with a cesium sulfate linear density and viscosity gradient which is introduced for boundary stabilization. The cell performance is illustrated with the centrifugal characterization of a polydisperse hyaluronate solution and a paucidisperse proteoglycan A1 preparation. In the latter case a distinctive distribution of aggregates into two polydisperse families of molecules, hitherto not reported in the literature but previously observed with cylindrical cells in this laboratory, has been clearly confirmed. Analysis of plateau dilution during centrifugation indicated absence of artifacts.

Centrifugation, Density Gradient↗
PubMed2006

Illusory color mixing upon perceptual fading and filling-in does not result in 'forbidden colors'.

A retinally stabilized object readily undergoes perceptual fading. It is commonly believed that the color of the apparently vanished object is filled in with the color of the background because the features of the filled-in area are determined by features located outside the stabilized boundary. Crane, H. D., & Piantanida, T. P. (1983) (On seeing reddish green and yellowish blue. Science, 221, 1078-1080) reported that the colors that are perceived upon full or partial perceptual fading can be 'forbidden' in the sense that they violate color opponency theory. For example, they claimed that their subjects could perceive "reddish greens" and "yellowish blues." Here we use visual stimuli composed of spatially alternating stripes of two different colors to investigate the characteristics of color mixing during perceptual filling-in, and to determine whether 'forbidden colors' really occur. Our results show that (1) the filled-in color is not solely determined by the background color, but can be the mixture of the background and the foreground color; (2) apparent color mixing can occur even when the two colors are presented to different eyes, implying that color mixing during filling-in is in part a cortical phenomenon; and (3) perceived colors are not 'forbidden colors' at all, but rather intermediate colors.

Adult↗
PubMed1997

Harvesting in discrete-time predator-prey systems.

Fisheries for assemblages of interacting species with seasonal recruitment occur throughout temperate and boreal regions of the world ocean. Such systems are conveniently modeled within a difference-equation framework. Here, we examine the dynamic behavior of discrete-time models for an exploited predator-prey system. We contrast the dynamic properties of an aggregate production model and an age-structured model in which recruitment and mortality are explicitly considered. The joint effects of harvesting and interspecific interactions on the stability of the system are defined and contrasted with results for single species systems. We demonstrate that harvesting is a potentially stabilizing factor in the production model and in an age-structured model in which juveniles are harvested and that the relative magnitude of the interaction between predator and prey strongly affects the exploitation levels at which stabilization occurs. In contrast, harvesting is potentially destabilizing (i.e., results in complex dynamics) in an age-structured model with harvesting of adults only; again, the magnitude of the interaction determines the stability boundaries, with stronger interactions leading to a broader range of stable parameter space. In both the aggregate production model and the age-structured model with harvesting of juvenile predator and prey, exploitation effectively reduces the intrinsic rate of increase of the populations; for prey, this effect is amplified by high predation mortality rates. Sustainable levels of exploitation for both predators and prey are lower for the case where juveniles are harvested. Predators and resource harvesters can be viewed as competitors for the prey, and sustainable harvest levels are directly affected by the magnitude of predation mortality. These considerations expand the scope of issues to be resolved in fishery management to include factors such as trade-offs between mean yield and the potential for intrinsic variability and the role of predator-prey interactions in shaping the dynamics of exploited systems.

Age Factors↗
PubMed2003

H/D exchange of gas phase bradykinin ions in a linear quadrupole ion trap.

The gas phase H/D exchange reaction of bradykinin ions, as well as fragment ions of bradykinin generated through collisions in an orifice skimmer region, have been studied with a linear quadrupole ion trap (LIT) reflectron time-of-flight (rTOF) mass spectrometer system. The reaction in the trap takes only tens of seconds at a pressure of few mTorr of D2O or CD3OD. The exchange rate and hydrogen exchange level are not sensitive to the trapping q value over a broad range, provided q is not close to the stability boundary (q = 0.908). The relative rates and hydrogen exchange levels of protonated and sodiated +1 and +2 ions are similar to those observed previously by others with a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer system. The doubly and triply protonated ions show multimodal isotopic distributions, suggesting the presence of several different conformations. The y fragment ions show greater exchange rates and levels than a or b ions, and when water or ammonia is lost from the fragment ions, no exchange is observed.

Bradykinin↗
PubMed2005

Oxidation of hydroxylamine by nitrous and nitric acids. Model development from first principle SCRF calculations.

Ab initio molecular orbital calculations have been performed to develop an elementary reaction mechanism for the autocatalytic and scavenging reactions of hydroxylamine in an aqueous nitric acid medium. An improved understanding of the titled reactions is needed to determine the "stability boundary of hydroxylamine" for safe operations of the plutonium-uranium reduction extraction (PUREX) process. Under the operating conditions of the PUREX process, namely, 6 M nitric acid, the reactive forms of hydroxylamine are NH2OH, NH3OH+, and the complex NH3OH.NO3, and those of nitrous acid are NO+, H2ONO+, N2O4, N2O3, NO2, and NO. High-level CBSQB3/IEFPCM and CBSQB3/COSMO calculations were performed using GAUSSIAN03 to investigate the energy landscape and to explore a large number of possible ion-ion, ion-radical, ion-molecule, radical-radical, radical-molecule, and molecule-molecule pathways available to the reactive forms of the reactants in solution. It was found that in solution the autocatalytic generation of nitrous acid proceeds through free radical pathways at low-hydroxylamine concentrations from unprotonated NH2OH via hydrogen abstraction. At high [NH3OH+], we suggest a possible involvement of the NH3ONO+ intermediate via the reaction NH2ONO + NO2 --> HNO + HONO + NO. The NH3ONO+ intermediate, in turn, is formed favorably via the ion-ion reactions of NH3OH+ with NO+ and/or the reaction between NO+ and hydroxylammonium nitrate (HAN). The intermediates involved in the scavenging reaction of nitrous acid by hydroxylamine are NH3ONO+, NH2ONO, NH2(NO)O, NH(NO)OH, and HONNOH and the rate-determining step is the 1,2-NO migration in NH2ONO leading to NH2(NO)O. Reactions NH2ONO --> NH2(NO)O and NH2(NO)O --> NH(NO)OH were studied with two explicit water molecules and the results are discussed in the context of the importance of the explicit treatment of solvent in the determination of the energetics and mechanism of these processes. The rate constants for the reactions were estimated using transition-state theory and other traditional techniques. The kinetic parameters obtained at the B3LYP/CBSB7/IEFPCM level are in reasonable agreement with the limited experimental value. IEFPCM results on free energy of undelocalized polar ions such as NO3-, NO2-, and NH3OH+ are not very accurate and have difficulties in predicting the right direction of acid dissociation equilibrium of HONO2, HONO, and NH3OH+. Explicit incorporation of a solvation shell to these ions improves the theoretical descriptions of acid ionization equilibria as it captures some of the nonlocal effects of these ions. Additional work is needed to correctly describe the solvation shell and to introduce consistency in the theoretical treatment involving explicit solvent molecules. Nevertheless, this systematic exploration of reactions in solution and mechanism development for a solution phase process based on self-consistent reaction field (SCRF) results is likely to be one of the first of its kind.

Journal Article↗
PubMed2003

Theoretical study of stability problems for transport in a deformable microfabricated channel.

We investigate the stability problem related to the basic flows induced by peristaltic transport within the bounded deformable walls which are common in micro- andor nanobiotechnological applications. The neutral stability boundary is obtained by solving the relevant Orr-Sommerfeld equation via a verified preconditioned complex-matrix solver. The critical Reynolds number (when the wall is deformable) is 2886.5 which is much less than the conventional rigid-wall case ( approximately 5772, obtained by Orszag based on the spectral method).

Journal Article↗
PubMed1992

Coupled maps and pattern formation on the Sierpinski gasket.

The bifurcation structure of coupled maps on the Sierpinski gasket is investigated. The fractal character of the underlying lattice gives rise to stability boundaries for the periodic synchronized states with unusual features and spatially inhomogeneous states with a complex structure. The results are illustrated by calculations on coupled quadratic and cubic maps. For the coupled cubic map lattice bistability and domain growth processes are studied.

Journal Article↗
PubMed2004

Global dynamics of low immersion high-speed milling.

In the case of low immersion high-speed milling, the ratio of time spent cutting to not cutting can be considered as a small parameter. In this case the classical regenerative vibration model of machine tool vibrations reduces to a simplified discrete mathematical model. The corresponding stability charts contain stability boundaries related to period doubling and Neimark-Sacker bifurcations. The subcriticality of both types of bifurcations is proved in this paper. Further, global period-2 orbits are found and analyzed. In connection with these orbits, the existence of chaotic motion is demonstrated for realistic high-speed milling parameters.

Journal Article↗
PubMed1999

Theory of modulational instability in Bragg gratings with quadratic nonlinearity.

Modulational instability in optical Bragg gratings with a quadratic nonlinearity is studied. The electric field in such structures consists of forward and backward propagating components at the fundamental frequency and its second harmonic. Analytic continuous wave (CW) solutions are obtained, and the intricate complexity of their stability, due to the large number of equations and number of free parameters, is revealed. The stability boundaries are rich in structures and often cannot be described by a simple relationship. In most cases, the CW solutions are unstable. However, stable regions are found in the nonlinear Schrödinger equation limit, and also when the grating strength for the second harmonic is stronger than that of the first harmonic. Stable CW solutions usually require a low intensity. The analysis is confirmed by directly simulating the governing equations. The stable regions found have possible applications in second-harmonic generation and dark solitons, while the unstable regions may be useful in the generation of ultrafast pulse trains at relatively low intensities.

Journal Article↗
PubMed2000

Synchronization of chaos in coupled systems

The stability of synchronous chaos of coupled oscillators with diffusive and gradient couplings is investigated. The stability boundaries of all transverse modes can be simultaneously drawn by justifying the boundary of a single mode, according to a scaling relation. Therefore, the distribution of stable and unstable regions can be explicitly shown in control parameter space. Bifurcations through different unstable modes, leading to different spatial orders, are analyzed.

Journal Article↗
PubMed2000

Surface stability of granular systems under horizontal and vertical vibration: the applicability of a coefficient of friction

We investigate the conditions under which the surface of a granular pile becomes unstable to vibrations. Three stability boundaries are identified, which depend upon the relative phase of the driving forces and the angle of the prepared slope. The experimental findings can be interpreted within the context of a Coulomb friction model and used to define an effective coefficient of friction. For up-hill motion we find that the coefficient of friction depends strongly on the slope angle and that, in general, it requires less vibration to transport grains uphill than would be otherwise expected.

Journal Article↗
PubMed2001

Model for interacting instabilities and texture dynamics of patterns.

A simple model to study interacting instabilities and textures of resulting patterns for thermal convection is presented. The model, consisting of a twelve-mode dynamical system derived for periodic square lattice, describes convective patterns in the form of stripes and patchwork quilt. The interaction between stationary zigzag stripes and standing patchwork quilt pattern leads to spatiotemporal patterns of twisted patchwork quilt. Textures of these patterns, which depend strongly on Prandtl number, are investigated numerically using the model. The model also shows an interesting possibility of a multicritical point, where stability boundaries of four different structures meet.

Journal Article↗
PubMed2002

Sequential bifurcations in sheared annular electroconvection.

A sequence of bifurcations is studied in a one-dimensional pattern forming system subject to the variation of two experimental control parameters: a dimensionless electrical forcing number R and a shear Reynolds number Re. The pattern is an azimuthally periodic array of traveling vortices with integer mode number m. Varying R and Re permits the passage through several codimension-two (CoD2) points. We find that the coefficients of the nonlinear terms in a generic Landau equation for the primary bifurcation are discontinuous at the CoD2 points. Further, we map the stability boundaries in the space of the two parameters by studying the subcritical secondary bifurcations in which m-->m+1 when R is increased at constant Re.

Journal Article↗
PubMed2004

Synchronization of two interacting populations of oscillators.

We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment, and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed.

Adaptation, Physiological↗