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stability

stability A multidiscipline term with a variety of (related) meanings. In numerical analysis it is used with what appears to be a bewildering array of possible prefixes. There are, however, two important basic usages.

Given a well-defined numerical procedure it is important that roundoff errors do not seriously influence the accuracy of the results. This is referred to as numerical stability and depends on the error-propagation properties of the procedure.

Discretization methods for the solution of integral and differential equations are based on a subdivision of the region in which the solution is required. Stability here means that perturbations in the data (initial or boundary conditions) have a bounded effect on the solution obtained (ignoring roundoff error) for a given subdivision. The existence of a uniform bound on this effect over all sufficiently fine subdivisions is a necessary condition for the convergence of the method as the subdivision is refined.

In the solution of ordinary differential equations much of the stability theory has been developed in the study of stiff systems of equations. Of great importance to this development was the concept of A-stability introduced by Dahlquist in 1963. A method is A-stable if it produces bounded solutions for the test problem y′ = qy, y(0) = 1 Re(q) < 0

for all stepsizes. The trapezoidal rule (see ordinary differential equations) is an example of an A-stable method. Much of the later theory has investigated similar properties for more general test problems.

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stability

stability
1. Atmospheric condition in which air that is forced to rise tends to return to its pre-existing position in the absence of the uplifting force. If the adiabatic lapse rate of uplifted air is greater than the environmental lapse rate, then the vertically displaced air will become colder than the surrounding air and as its density increases it will tend to sink back. See also INSTABILITY.

2. In engineering, the resistance of a structure to collapse or sliding, dependent upon the shearing strength of the material.

3. In geochemistry, the state of equilibrium towards which a system will move from any other state under the same conditions.

4. In thermodynamics, the condition when a slight disturbance of temperature, pressure, or composition does not result in the appearance of a new phase.

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stability

stability An atmospheric condition in which air that is forced to rise tends to return to its pre-existing level in the absence of the uplifting force. If the adiabatic lapse rate of uplifted air is greater than the environmental lapse rate, the vertically displaced air will become colder than the surrounding air and as its density increases it will tend to sink back. Compare instability.

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stability

sta·bil·i·ty / stəˈbilitē/ • n. the state of being stable: there are fears for the political stability of the area.

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stability

stability: see equilibrium.

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stability

stabilitybanditti, bitty, chitty, city, committee, ditty, gritty, intercity, kitty, nitty-gritty, Pitti, pity, pretty, shitty, slitty, smriti, spitty, titty, vittae, witty •fifty, fifty-fifty, nifty, shifty, swiftie, thrifty •guilty, kiltie, silty •flinty, linty, minty, shinty •ballistae, Christie, Corpus Christi, misty, twisty, wristy •sixty •deity, gaiety (US gayety), laity, simultaneity, spontaneity •contemporaneity, corporeity, femineity, heterogeneity, homogeneity •anxiety, contrariety, dubiety, impiety, impropriety, inebriety, notoriety, piety, satiety, sobriety, ubiety, variety •moiety •acuity, ambiguity, annuity, assiduity, congruity, contiguity, continuity, exiguity, fatuity, fortuity, gratuity, ingenuity, perpetuity, perspicuity, promiscuity, suety, superfluity, tenuity, vacuity •rabbity •improbity, probity •acerbity • witchetty • crotchety •heredity •acidity, acridity, aridity, avidity, cupidity, flaccidity, fluidity, frigidity, humidity, hybridity, insipidity, intrepidity, limpidity, liquidity, lividity, lucidity, morbidity, placidity, putridity, quiddity, rabidity, rancidity, rapidity, rigidity, solidity, stolidity, stupidity, tepidity, timidity, torpidity, torridity, turgidity, validity, vapidity •commodity, oddity •immodesty, modesty •crudity, nudity •fecundity, jocundity, moribundity, profundity, rotundity, rubicundity •absurdity • difficulty • gadgety •majesty • fidgety • rackety •pernickety, rickety •biscuity •banality, duality, fatality, finality, ideality, legality, locality, modality, morality, natality, orality, reality, regality, rurality, tonality, totality, venality, vitality, vocality •fidelity •ability, agility, civility, debility, docility, edibility, facility, fertility, flexility, fragility, futility, gentility, hostility, humility, imbecility, infantility, juvenility, liability, mobility, nihility, nobility, nubility, puerility, senility, servility, stability, sterility, tactility, tranquillity (US tranquility), usability, utility, versatility, viability, virility, volatility •ringlety •equality, frivolity, jollity, polity, quality •credulity, garrulity, sedulity •nullity •amity, calamity •extremity • enmity •anonymity, dimity, equanimity, magnanimity, proximity, pseudonymity, pusillanimity, unanimity •comity •conformity, deformity, enormity, multiformity, uniformity •subcommittee • pepperminty •infirmity •Christianity, humanity, inanity, profanity, sanity, urbanity, vanity •amnesty •lenity, obscenity, serenity •indemnity, solemnity •mundanity • amenity •affinity, asininity, clandestinity, divinity, femininity, infinity, masculinity, salinity, trinity, vicinity, virginity •benignity, dignity, malignity •honesty •community, immunity, importunity, impunity, opportunity, unity •confraternity, eternity, fraternity, maternity, modernity, paternity, taciturnity •serendipity, snippety •uppity •angularity, barbarity, bipolarity, charity, circularity, clarity, complementarity, familiarity, granularity, hilarity, insularity, irregularity, jocularity, linearity, parity, particularity, peculiarity, polarity, popularity, regularity, secularity, similarity, singularity, solidarity, subsidiarity, unitarity, vernacularity, vulgarity •alacrity • sacristy •ambidexterity, asperity, austerity, celerity, dexterity, ferrety, posterity, prosperity, severity, sincerity, temerity, verity •celebrity • integrity • rarity •authority, inferiority, juniority, majority, minority, priority, seniority, sonority, sorority, superiority •mediocrity • sovereignty • salubrity •entirety •futurity, immaturity, impurity, maturity, obscurity, purity, security, surety •touristy •audacity, capacity, fugacity, loquacity, mendacity, opacity, perspicacity, pertinacity, pugnacity, rapacity, sagacity, sequacity, tenacity, veracity, vivacity, voracity •laxity •sparsity, varsity •necessity •complexity, perplexity •density, immensity, propensity, tensity •scarcity • obesity •felicity, toxicity •fixity, prolixity •benedicite, nicety •anfractuosity, animosity, atrocity, bellicosity, curiosity, fabulosity, ferocity, generosity, grandiosity, impecuniosity, impetuosity, jocosity, luminosity, monstrosity, nebulosity, pomposity, ponderosity, porosity, preciosity, precocity, reciprocity, religiosity, scrupulosity, sinuosity, sumptuosity, velocity, verbosity, virtuosity, viscosity •paucity • falsity • caducity • russety •adversity, biodiversity, diversity, perversity, university •sacrosanctity, sanctity •chastity •entity, identity •quantity • certainty •cavity, concavity, depravity, gravity •travesty • suavity •brevity, levity, longevity •velvety • naivety •activity, nativity •equity •antiquity, iniquity, obliquity, ubiquity •propinquity

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Stability

Stability


The term "stability" refers to the tendency of an individual organism, a community, a population, or an ecosystem to maintain a more or less constant structure over relatively long periods of time. Stability does not suggest that changes do not occur, but that the net result of those changes is nearly zero. A healthy human body is an example of a stable system. Changes are constantly taking place in a body. Cells die and are replaced by new ones. Chemical compounds are manufactured in one part of the body and degraded in another part. But, in spite of these changes, the body tends to look very much the same from day to day, week to week, and month to month.

The same is true with groups of individuals. A prairie grassland may look the same from year to year, even though the individual plants that make up the community change. Many ecosystems exhibit mosaic stability. For instance, a forest with openings caused by windthrow or fire at different times regrows trees of the same species ,so that the character of the forest remains unchanged.

Stability is threatened by various kinds of stress. For example, lack of food can threaten the stability of an individual person, and fire can endanger the stability of a grassland community. Both organisms and communities have a rather remarkable resilience to such threats, however, and are often able to return to their original structure. Given good food once again, a person can recover her or his health and structure, just as a grassland tends to regrow after a fire.

The biotic and abiotic elements of an ecosystem cause stress on each other which can threaten the stability of each. An unusually long dry spell, for example, can cause plants to die and endanger the biotic community's stability. In turn, animals may multiply in number and physically degrade the soil and water in their habitat .

Because of the magnitude of the stress they place on other communities, humans are often the most serious threat to the stability of an ecosystem. An old-growth forest that has been clear-cut may, in theory, restore itself eventually to its original structure. But the time frame needed for such a restoration involves hundreds or thousands of years. For all practical purposes, therefore, the community of organisms in the region has ceased to exist as such.

One of the important mechanisms by which ecosystems maintain stability is negative feedback. Suppose, for example, that favorable weather conditions cause an unusually large growth of plants in a valley. Animals that live on those plants, then, will also increase in number and reproduce in greater quantity than in less abundant years. The increased population of animals will place a severe stress on the plant community if and when weather conditions return to normal. With decreased food supplies per individual organism, more animals will die off and the population will return to its previous size.

The factors that contribute to the stability of an ecosystem are not well-understood. At one time, most scholars accepted the hypothesis that diversity was an important factor in maintaining stability. From a common sense perspective, it is reasonable to assume that the more organisms and more kinds of organisms in a system, the greater the distribution of stress and the more stable the system as a whole will be.

Some early experiments appeared to confirm this view, but those experiments were often conducted with artificial or only simplified systems. Ecologists are increasingly beginning to question the relationship between biodiversity and stability, at least partly because of examples from the real world. Some highly complex systems, such as tropical rain forests , have been less successful in responding to external stress than have simpler systems, such as tundra .

The term "stability" has a more specialized meaning in atmospheric studies. There, it also refers to a condition in which vertical layers of air at different temperatures are in equilibrium with each other.

See also Population biology

[David E. Newton ]


RESOURCES

BOOKS

Clapham Jr., W. B. Natural Ecosystems. New York: The Macmillan Company, 1973.

Suthers, R. A., and R. A. Gallant. Biology: The Behavioral View. Lexington, MA: Xerox College Publishing, 1973.

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