Logistical growth

Fig. 4-11 Shaj>e of "logistical growth." The rate of change increases slowly initially. The rate of growth reaches a maximum and eventually drops to zero as the mass levels off, approaching the value A/B.

K, logistic growth curve constant K, logistic growth curve constant Volume, allometric exponents Liver Kidney Bone... 

Logistic growth curve, where log Y = A/( + Bpx), such as a population growth curve. 

The degree of nitrification did not increase linearly with residence time, but was more of a step change. The accumulation of nitrified oxygen (N02 +N03 ) was described by a logistic growth curve (20), in the range of residence times 2.1 to 4.1 days ... 

Tectonic Realms Steady-State Since 4500 x 106 y Ago "Preferred" or Logistic Growth Model Theoretical Half-L (T50) x 10 y... 

It appears from the above that microcosm and/or mesocosm tests are limited by the constraints of experimentation, in that usually only a limited number of recovery scenarios can be investigated. Consequently, modeling approaches may provide an alternative tool for investigating likely recovery rates under a range of conditions. Generic models, like the logistic growth mode (for example, see Barnthouse 2004) and life history and individual-based (meta)population models, which also may be spatially explicit, provide mathematical frameworks that offer the opportunity to explore the recovery potential of individual populations. For an overview of these life history and individual-based models, see Bartell et al. (2003) and Pastorok et al. (2003). 

Yano Y, Oguma T, Nagata H, Sasaki S. Application of a logistic growth model to pharmacodynamic analysis of in vitro bactericidal kinetics. J Pharm Sci 1998 87 1177-83. 

The growth of a bacteria Stepinpoopi can be described by die logistic growth law... 

Alternative models of cell growth dynamics may be substituted for Eq. (23.4) and tested using standard model fitting criteria. For example, in vitro and in vivo cell populations rarely continue to grow exponentially as a result of spatial, nutritive, and other factors that may place an upper limit on cell density (Rss). The logistic growth model is one function that limits exponential growth and is defined as (7)... 

We mention also that the same dynamics of logistic growth and saturation can be obtained by combining the autocatalytic reaction (3.19) with its inverse ... 

A common way to address the first caveat is to replace the growth term a P for the prey in (3.68) by a more realistic logistic growth (3.66). For the second, it is natural to replace the interaction terms ZP in (3.68)-(3.69) by more general forms. This leads to... 

Fisher (1937), proposed an equation combining the logistic growth mechanism of (3.9), (3.23) or (3.66) with diffusion to model the spatial spreading of favorable genes in a population distributed in one dimension ... 

Figure 6.1 Average plankton population density as a function of the Damkohler number for logistic growth with non-uniform carrying capacity of the form K(x,y) = Kq + (5sin(27rx) sin(27ry) and chaotic mixing in the time-periodic sine-flow of Eq. (2.66). The continuous line represents results from the solution of the full partial differential equation with diffusion (Pe 104) and stars ( ) show the time-averaged plankton populations calculated from the non-diffusive Lagrangian representation.

The dependence of the average concentration on the Damkohler number can also be interpreted within the Lagrangian formulation. For example, the logistic growth function of the plankton population dynamics (Eq. (6.7)) is concave near the steady state P = K, i.e. the plankton population reacts more quickly when the carrying capacity is below the actual plankton density, than in the opposite case when higher carrying capacity allows for increase of the plankton concentration. Due to this asymmetric nonlinear response the... 

For packed beds without internal heat transfer a modified Damkohler number (DaM) can be proposed assiuning logistic growth kinetics without maintenance metabohsm [142] ... 

Models available linear, logarithmic, inverse, quadratic, cubic, power, compound. S-curve. logistic, growth, exponential... 

Almost parallel to McKendrick, Hutchinson [215], a well-known ecologist, proposed a time-delayed version for the logistic growth equation, where the nonlinear term was delayed in time. The diffusive Hutchinson equation, also known as the delayed Fisher equation. 

Consider particles that follow a CTRW, such that the random time T between jumps is exponentially distributed with rate X, f(T > t) = exp(—A.t). The mean-field equation for the particle density is the Master equation for the compound Poisson process with logistic growth (5.2), Hyperbolic scaling yields... 

We assume that the population growth can be described by the logistic growth function F p) = p( - /o/Pmax) where p is the saturation density or carrying capacity. This growth function compares favorably with a wealth of experimental results [256]. Equation (7.1) leads to wavefronts with asymptotic velocity, see (5.60),... 

Figure 7.11 summarizes the results obtained from (7.42) (lines) and compares it with random walk simulations on the Peano basin up to order Q = 10 (open circles) and OCNs (full circles). In the simulations, all the walkers were initially on the left side of the lattice and the front advanced to the right. A logistic growth rp(l — p) was introduced at every site at every time step to simulate the reaction process. For the OCNs, we averaged over 10 different 200 x 200 networks. 

The replication process begins when the virus injects its DNA into the bacterium. The latter replicates the viral DNA and new viruses are formed. They are released into the medium by bursting the bacteria and the lytic cycle ends. Replication phenomena match very well a logistic growth of vimses, and we assume... 

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