共查询到20条相似文献,搜索用时 31 毫秒
1.
C. Z. Roux 《Theoretical population biology》1974,5(3):393-416
The structure of multiloci random mating populations is examined. Sufficient conditions for the existence of stable local Hardy-Weinberg equilibria for n loci and an arbitrary number of alleles per locus, are then derived for specified situations under the assumption of multiplicative gene action between loci. It is shown that a stable Hardy-Weinberg equilibrium can not be a local maximum of the mean fitness function with multiplicative gene action between loci. The stability of Hardy-Weinberg type border points and the condition for the increase of newly introduced genes are topics on which some n-loci results are also obtained for an arbitrary number of alleles per locus in systems that allow Hardy-Weinberg equilibria. 相似文献
2.
N. Rashevsky 《Bulletin of mathematical biology》1971,33(2):157-164
In classical physics the stability of an equilibrium requires that any, even infinitesimal, displacement from the configuration
of equilibrium results in forces which tend to restore the original equilibrium configuration. In case of several stable equilibrium
configurations, the height of the threshold, which must be exceeded by the deviarion from the stable equilibrium in order
to bring the configuration into another stable equilibrium is taken as a measure of stability of the first configuration.
In quantum mechanics, and in the recent work of I. Baianu, S. Comorosan and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968;31, 59–70, 1969;32, 539–561, 1970) on organismic supercategories, preference is given to take, as ameasure of the degree of stability of a configuration,
or of a “state”, the length of time during which the system remains in that configuration. It is shown that under rather general
conditions the two criteria are equivalent. 相似文献
3.
J. M. Cushing 《Journal of mathematical biology》1984,20(3):259-276
The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population
is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the
trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional
of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in
the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of
the author.
The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability.
It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical.
Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states
as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield
formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates
as functionals of population density.
Analytical and numerical results for some examples are given which illustrate these results. 相似文献
4.
Alan M. Weinstein 《Bulletin of mathematical biology》1992,54(4):537-561
An epithelial cell is modeled as a single compartment, bounded by apical and basolateral cell membranes, and containing two
nonelectrolyte solute species, nominally NaCl and KCl. Membrane transport of these species may be metabolically driven, or
it may follow the transmembrane concentration gradients, either singly (a channel) or jointly (a cotransporter). To represent
the effect of stretch-activated channels or shrinkage-activated cotransporters, the membrane permeabilities and cotransport
coefficients are permitted to be functions of cell volume. When this epithelium is considered as a dynamical system, conditions
are indicated which guarantee the uniqueness and stability of equilibria. Experimentally, many epithelial cells can regulate
their volume, and such volume regulatory capability is defined for this model. It is clearly distinct from dynamical stability
of the equilibrium and requires more stringent conditions on the volume-dependent permeabilities and cotransporters. For a
previously developed model of the toad urinary bladder (Strieteret al., 1990,J. gen. Physiol.
96, 319–344) the uniqueness and stability of its equilibria are indicated. The analysis also demonstrates that under some conditions
a second stable equilibrium may appear, along with a saddle-node bifurcation. This is illustrated numerically in a modified
model of the epithelium of the thick ascending limb of Henle. 相似文献
5.
Craig J. Benham 《Biopolymers》1983,22(11):2477-2495
This paper analyzes the elastic equilibrium conformations of duplex DNA constrained by the constancy of its molecular linking number, Lk. The DNA is regarded as having the mechanical properties of a homogeneous, linearly elastic substance with symmetric cross section. Integral representations of the writhing number Wr and of Lk are developed, in terms of which the equilibria are given as solutions to an isoperimetric problem. It is shown that the Euler angles defining equilibrium conformations must obey equations identical to those governing unconstrained equilibria. A scaling law is developed stating that molecules supercoiled the same amount ΔLk will have geometrically similar elastic equilibria regardless of their length. Thus, comparisons among molecules of properties related to their large-scale tertiary structure should be referred to differences in ΔLk rather than to their superhelix densities. Specific conditions on the elastic equilibrium conformations are developed that are necessary for ring closure. The equilibrium superhelical conformations accessible to closed-ring molecules are shown to approximate toroidal helices. Questions relating to the stability and nonuniqueness of equilibria are treated briefly. A comparison is made between these toroidal conformations and interwound configurations, which are shown to be stable, although they are not equilibria in the present sense. It is suggested that entropic factors are responsible for favouring the toroidal conformation in solution. 相似文献
6.
F. B. Christiansen 《Journal of mathematical biology》1988,26(6):595-618
The n-locus two-allele symmetric viability model is considered in terms of the parameters measuring the additive epistasis in fitness. The dynamics is analysed using a simple linear transformation of the gametic frequencies, and then the recurrence equations depend on the epistatic parameters and Geiringer's recombination distribution only. The model exhibits an equilibrium, the central equilibrium, where the 2
n
gametes are equally frequent. The transformation simplifies the stability analysis of the central point, and provides the stability conditions in terms of the existence conditions of other equilibria. For total negative epistasis (all epistatic parameters are negative) the central point is stable for all recombination distributions. For free recombination either a central point (segregating one, two, ... or n loci) or the n-locus fixation states are stable. For no recombination and some epistatic parameters positive the central point is unstable and several boundary equilibria may be locally stable. The sign structure of the additive epistasis is therefore an important determinant of the dynamics of the n-locus symmetric viability model. The non-symmetric multiple locus models previously analysed are dynamically related, and they all have an epistatic sign structure that resembles that of the multiplicative viability model. A non-symmetric model with total negative epistasis which share dynamical properties with the similar symmetric model is suggested.Supported in part by NIH grant GM 28016, and by grant 81-5458 from the Danish Natural Science Research Council 相似文献
7.
Alston S. Householder 《Bulletin of mathematical biology》1941,3(1):27-38
Rashevsky's equations for describing the joint variation of cell shape and concentration of a metabolite are discussed. Conditions
for the existence of non-spherical equilibria and the location of these are obtained and involve only two parametersa andA. Sufficient (but not necessary) conditions for the stability of these equilibria can also be expressed in terms of these
parameters alone. Necessary conditions involve in some cases a third parameterB. Quasi-periodic fluctuations about a stable nonspherical equilibrium may occur, but only in caseB lies on a certain finite range which can be defined in terms ofa andA. 相似文献
8.
Cain JW 《Journal of mathematical biology》2007,55(3):433-448
We model electrical wave propagation in a ring of cardiac tissue using an mth-order difference equation, where m denotes the number of cells in the ring. Under physiologically reasonable assumptions, the difference equation has a unique
equilibrium solution. Applying Jury’s stability test, we prove a theorem concerning the local asymptotic stability of this
equilibrium solution. Our results yield conditions for sustained reentrant tachycardia, a type of cardiac arrhythmia.
相似文献
9.
Jan Prüß 《Journal of mathematical biology》1981,11(1):65-84
Summary A mathematical model describing the dynamics of a population consisting of several species is studied. The interactions in the population are assumed to be age-specific. Using an evolution equation approach, sufficient conditions for well-posedness in L
1 of the dynamics and for existence as well as for stability of equilibrium solutions are given. 相似文献
10.
This paper presents a resource-dependent viability selection differential equation model of continuously reproducing diploid population with two alleles at one locus for a single limiting resource. This model assumes that the genotypic fitness is only a function of the limiting resource. The conditions that the interior equilibrium point of the system exists are that the heterozygote fitness is positive and the homozygote fitness is negative, or the heterozygote fitness is negative and the homozygote fitness is positive at the point. The sufficient and necessary conditions of locally asymptotical stability of the interior equilibrium point are that the heterozygote fitness is positive at the point, or the locally asymptotically stable equilibrium corresponds to the point at which the level of the limiting resource is locally minimized on the zero mean fitness curve, f = 0. 相似文献
11.
Stability analysis of pathogen-immune interaction dynamics 总被引:2,自引:0,他引:2
The paper considers models of dynamics of infectious disease in vivo from the standpoint of the mathematical analysis of stability. The models describe the interaction of the target cells, the pathogens, and the humoral immune response. The paper mainly focuses on the interior equilibrium, whose components are all positive. If the model ignores the absorption of the pathogens due to infection, the interior equilibrium is always asymptotically stable. On the other hand, if the model does consider it, the interior equilibrium can be unstable and a simple Hopf bifurcation can occur. A sufficient condition that the interior equilibrium is asymptotically stable is obtained. The condition explains that the interior equilibrium is asymptotically stable when experimental parameter values are used for the model. Moreover, the paper considers the models in which uninfected cells are involved in the immune response to pathogens, and are removed by the immune complexes. The effect of the involvement strongly affects the stability of the interior equilibria. The results are shown with the aid of symbolic calculation software. 相似文献
12.
Chrzanowski F 《AAPS PharmSciTech》2008,9(2):639-645
Practical examples of preformulation support of the form selected for formulation development are provided using several drug
substances (DSs). The examples include determination of the solubilities vs. pH particularly for the range pH 1 to 8 because of its relationship to gastrointestinal (GI) conditions and dissolution
method development. The advantages of equilibrium solubility and trial solubility methods are described. The equilibrium method
is related to detecting polymorphism and the trial solubility method, to simplifying difficult solubility problems. An example
of two polymorphs existing in mixtures of DS is presented in which one of the forms is very unstable. Accelerating stability
studies are used in conjunction with HPLC and quantitative X-ray powder diffraction (QXRD) to demonstrate the differences
in chemical and polymorphic stabilities. The results from two model excipient compatibility methods are compared to determine
which has better predictive accuracy for room temperature stability. A DSC (calorimetric) method and an isothermal stress
with quantitative analysis (ISQA) method that simulates wet granulation conditions were compared using a 2 year room temperature
sample set as reference. An example of a pH stability profile for understanding stability and extrapolating stability to other
environments is provided. The pH-stability of omeprazole and lansoprazole, which are extremely unstable in acidic and even
mildly acidic conditions, are related to the formulation of delayed release dosage forms and the resolution of the problem
associated with free carboxyl groups from the enteric coating polymers reacting with the DSs. Dissolution method requirements
for CR dosage forms are discussed. The applicability of a modified disintegration time (DT) apparatus for supporting CR dosage
form development of a pH sensitive DS at a specific pH such as duodenal pH 5.6 is related. This method is applicable for DSs
such as peptides, proteins, enzymes and natural products where physical observation can be used in place of a difficult to
perform analytical method, saving resources and providing rapid preformulation support.
Presented at the 41st Annual Pharmaceutical Technologies Arden Conference—Oral Controlled Release Development and Technology,
January 2006, West Point NY. 相似文献
13.
A hierarchically structured population model with a dependence of the vital rates on a function of the population density
(environment) is considered. The existence, uniqueness and the asymptotic behaviour of the solutions is obtained transforming the original
non-local PDE of the model into a local one. Under natural conditions, the global asymptotical stability of a nontrivial equilibrium
is proved. Finally, if the environment is a function of the biomass distribution, the existence of a positive total biomass
equilibrium without a nontrivial population equilibrium is shown.
Received 16 February 1996; received in revised form 16 September 1996 相似文献
14.
R. M. Mitchell 《Biopolymers》1976,15(9):1741-1753
Exact expressions are obtained for the mean position and the variance about the mean of macromolecules which are moving in an electrostatic or centrifugal field and which, at the same time, are switching back and forth between two isomeric states. Comparison with experiment then yields the forward and backward switching rates. The following special cases are considered: (a) only one species present initially; (b) both species present initially but not in their equilibrium proportions; (c) both species present initially in their equilibrium proportions. It is shown that in the first two cases we need only measure the mean position of all the molecules in order to measure the absolute switching rates k1 and k2. In the third case, however, we must measure the variance (mean-square deviation) of the position in order to obtain k1 and k2. The first two situations arise when “jumps” (e.g., in temperature or pressure) are made, while the third situation is obtained if the experiment is conducted with the species in chemical equilibrium throughout the experiment. 相似文献
15.
考虑了CTLs免疫应答和细胞内部时滞建立HIV-1感染的数学模型.对模型的无感染平衡点全局稳定性进行了分析,对CTLs未激活和CTLs已激活的感染平衡点给出了局部稳定的充分条件.数值模拟支持了得到的理论结果. 相似文献
16.
Schneider KA 《Journal of mathematical biology》2006,52(4):483-523
The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele
model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number
of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well
as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection
to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation.
Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters.
It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient
conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit
formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection
is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population
size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model
in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria.
Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing
for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that
can occur if the assumption of additivity is relaxed. 相似文献
17.
Summary For a general multiple loop feedback inhibition system in which the end product can inhibit any or all of the intermediate reactions it is shown that biologically significant behaviour is always confined to a bounded region of reaction space containing a unique equilibrium. By explicit construction of a Liapunov function for the general n dimensional differential equation it is shown that some values of reaction parameters cause the concentration vector to approach the equilibrium asymptotically for all physically realizable initial conditions. As the parameter values change, periodic solutions can appear within the bounded region. Some information about these periodic solutions can be obtained from the Hopf bifurcation theorem. Alternatively, if specific parameter values are known a numerical method can be used to find periodic solutions and determine their stability by locating a zero of the displacement map. The single loop Goodwin oscillator is analysed in detail. The methods are then used to treat an oscillator with two feedback loops and it is found that oscillations are possible even if both Hill coefficients are equal to one. 相似文献
18.
讨论了一类具免疫时滞的HIV感染模型.分析了未感染平衡点的全局渐近稳定性,给出了感染无免疫平衡点及感染免疫平衡点局部渐近稳定的充分条件.数值模拟结果表明,当易感细胞生成率的取值使得基本再生数满足平衡存在的条件且低于某一临界值时,时滞对平衡点的稳定性没有影响;若大于该临界值,随着时滞增大,稳定性开关发生,平衡点不稳定,出现一系列Hopf分支,最终表现为周期波动模式. 相似文献
19.
Central Equilibria in Multilocus Systems. II. Bisexual Generalized Nonepistatic Selection Models 总被引:2,自引:1,他引:1
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This paper is a continuation of the paper "Central Equilibria in Multilocus Systems I," concentrating on existence and stability properties accruing to central H-W type equilibria in multilocus bisexual systems acted on by generalized nonepistatic selection forces coupled to recombination events. The stability conditions are discussed and interpreted in three perspectives, and the influence of sexual differences in linkage relationships together with sex-dependent selection is appraised. In this case we deduce that the stability conditions of the H-W polymorphism in the bisexual model coincide exactly with the conditions for the corresponding monoecious model, provided that the recombination distribution imposed is that of the arithmetic mean of the male and female recombination distributions. A second concern has the same recombination distribution for both sexes, but contrasting selection regimes between sexes. It is then established that, with respect to discerning the relevance of the H-W equilibrium, there is an equivalent monoecious selection regime which is an appropriate "weighted combination" of the male and female selection forms. Finally, in the case where the selection and recombination structures are both sex dependent, a hierarchy of comparisons is elaborated, seeking to unravel the nature of selection-recombination interaction for monoecious versus diocecious systems. 相似文献
20.
《Journal of biological dynamics》2013,7(1):278-287
ABSTRACTA stage-structured predator–prey system with distributed maturation delay and harvesting is investigated. General birth and death functions are used. The local stability of each feasible equilibria is discussed. By using the persistence theory, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functional and LaSalle invariant principle, it is shown that the trivial equilibrium is globally stable when the other equilibria are not feasible, and that the boundary equilibrium is globally stable if the coexistence equilibrium does not exist. Finally, sufficient conditions are derived for the global stability of the coexistence equilibrium. 相似文献