scholarly journals Approximate stationary densities, and parameter estimations for time-delayed stochastic logistic growth laws

2007 ◽  
Vol 47 ◽  
Author(s):  
Petras Rupšys
Keyword(s):  
Growth Model ◽  
Time Delays ◽  
Single Species ◽  
Small Time ◽  
Logistic Growth ◽  
Estimation Of Parameters ◽  
Stationary Distributions ◽  
Parameter Estimations ◽  
Growth Laws ◽  
Delayed Growth

We consider stochastic logistic type delayed growth model (Verhulst, Gompertz, Richards) of a single species population.The objective of this paper is to deduce a procedureon the estimation of parameters. We derive approximate stationary distributions in the case of small time delays. For the estimate of parameters we apply the L1 distance procedure. We propose approximate estimations of the parameters.

scholarly journals The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Carlo Bianca ◽  
Massimiliano Ferrara ◽  
Luca Guerrini
Keyword(s):  
Economic Growth ◽  
Growth Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Qualitative Behavior ◽  
Solow Model ◽  
Normal Form Theory ◽  
Economic Growth Model ◽  
Form Theory ◽  
The Stability

A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results.

Time Delays, Density-Dependence and Single-Species Oscillations

10.2307/3535 ◽  
1974 ◽  
Vol 43 (3) ◽  
pp. 747 ◽  
Author(s):  
R. M. May ◽  
G. R. Conway ◽  
M. P. Hassell ◽  
T. R. E. Southwood
Keyword(s):  
Density Dependence ◽  
Time Delays ◽  
Single Species

scholarly journals Extended logistic growth model for heterogeneous populations

2017 ◽  
Author(s):  
Wang Jin ◽  
Scott W McCue ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Growth Model ◽  
Numerical Solutions ◽  
Cellular Level ◽  
Logistic Growth ◽  
Logistic Growth Model ◽  
Living Tissues ◽  
Discrete Mathematical Model ◽  
The Continuum

AbstractCell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

scholarly journals Evolution of populations with strategy-dependent time delays

2019 ◽  
Author(s):  
Jacek Miȩkisz ◽  
Marek Bodnar
Keyword(s):  
Stationary State ◽  
Time Delays ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Small Time ◽  
Stochastic Perturbations ◽  
New Type ◽  
Novel Behavior

AbstractWe address the issue of stability of coexistence of two strategies with respect to time delays in evolving populations. It is well known that time delays may cause oscillations. Here we report a novel behavior. We show that a microscopic model of evolutionary games with a unique mixed evolutionarily stable strategy (a globally asymptotically stable interior stationary state in the standard replicator dynamics) and with strategy-dependent time delays leads to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, an interior stationary state of such dynamics depends continuously on time delays and at some point it might disappear, no cycles are present. In particular, this means that an arbitrarily small time delay changes an interior stationary state. Moreover, at certain time delays, there may appear another interior stationary state.Author summarySocial and biological processes are usually described by ordinary or partial differential equations, or by Markov processes if we take into account stochastic perturbations. However, interactions between individuals, players or molecules, naturally take time. Results of biological interactions between individuals may appear in the future, and in social models, individuals or players may act, that is choose appropriate strategies, on the basis of the information concerning events in the past. It is natural therefore to introduce time delays into evolutionary game models. It was usually observed, and expected, that small time delays do not change the behavior of the system and large time delays may cause oscillations. Here we report a novel behavior. We show that microscopic models of evolutionary games with strategy-dependent time delays, in which payoffs appear some time after interactions of individuals, lead to a new type of replicator dynamics. Unlike in all previous models, interior stationary states of such dynamics depend continuously on time delays. This shows that effects of time delays are much more complex than it was previously thought.

A Neoclassical Growth Model for Population Dynamics in a Homogeneous Habitat

2001 ◽  
Author(s):  
Peter Vadasz ◽  
Alisa S. Vadasz
Keyword(s):  
Experimental Data ◽  
Growth Model ◽  
Logistic Growth ◽  
Lag Phase ◽  
Growth Stages ◽  
Initial Growth ◽  
Neoclassical Model ◽  
Wide Range ◽  
Logistic Growth Model ◽  
Special Case

Abstract A neoclassical model is proposed for the growth of cell and other populations in a homogeneous habitat. The model extends on the Logistic Growth Model (LGM) in a non-trivial way in order to address the cases where the Logistic Growth Model (LGM) fails short in recovering qualitative as well as quantitative features that appear in experimental data. These features include in some cases overshooting and oscillations, in others the existence of a “Lag Phase” at the initial growth stages, as well as an inflection point in the “In curve” of the population size. The proposed neoclassical model recovers also the Logistic Growth Curve as a special case. Comparisons of the solutions obtained from the proposed neoclassical model with experimental data confirm its quantitative validity, as well as its ability to recover a wide range of qualitative features captured in experiments.

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