Population dynamics and utilitarian criteria in the Lucas–Uzawa Model (original) (raw)

Models of the World human population growth-critical analysis

We analyze mathematical models of the global human population growth and compare them to actual dynamics of the world population and of the world surplus product. We consider a possibility that the so-called world's demographic transition is not a dynamic crossover but a phase transition that affects all aspects of our life.

First Principles Attempt to Unify some Population Growth Models

arXiv: Populations and Evolution, 2016

In this work, some phenomenological models, those that are based only on the population information (macroscopic level), are deduced in an intuitive way. These models, as for instance Verhulst, Gompertz and Bertalanffy models, are posted in such a manner that all the parameters involved have physical interpretation. A model based on the interaction (distance dependent) between the individuals (microscopic level) is also presented. This microscopic model reachs the phenomenological models presented as particular cases. In this approach, the Verhulst model represents the situation in which all the individuals interact in the same way, regardless of the distance between them. That means Verhulst model is a kind of mean field model. The other phenomenological models are reaching from the microscopic model according to two quantities: i) the relation between the way that the interaction decays with the distance; and ii) the dimension of the spatial structure formed by the population. Thi...

An Investigation of the Logistic Model of Population Growth

2011

This article examines the popular logistic model of growth from three perspectives: its sensitivity to initial conditions; its relationship to analogous difference equation models; and the formulation of stochastic models of population growth where the mean population size satisfies the logistic relationship. The results indicate that the appealing sigmoid logistic curve is sensitive to initial conditions and care must be exercised in developing difference equation models which display the same appealing long term behavior as the logistic growth curve. It is shown that although the logistic model is appealing in terms of its simplicity its realism is questionable in terms of the degree to which it reflects demographically accepted assumptions about the probabilities of individual births and deaths in the growth of a population. In particular this lack of realism has serious implications for the computer simulation of stochastic birth and death processes where the mean population siz...

Some Propositions on Mathematical Models of Population Growth

2023

Some of the authors of this publication are also working on these related projects: RIEMANN HYPOTHESIS BY THE MEANS OF THE THEORY OF UNIVALENTFUNCTIONS AND ROBIN INEQUALITY View project Riemann Hypothesis: The only sharp result of Zeta function is location of the non trivial zeros View project

Rethinking the basis of the population growth

The paper goes back to the basis of population dynamics, especially the works of Malthus, and tries to model his pioneering vision again, this time taking into account such of his postulates as the necessity of food for survival, the reproduction of each individual and inequities of resource distribution. We construct a Conspecific Community Dynamics Model (CCDM), which is based on these well-known postulates of Malthus. Nevertheless, analysis of the model reveals quite interesting results. (1) The size of the community nontrivially depends on the level of equality between its members (for example, there is a given level of equality in which the size of the community becomes a maximum). (2) The size of the community is limited not only by the amount of resources, but the community's ability to utilize these resources. (3) A high level of equality leads to a dynamical instability, which, in turn, under certain conditions, may lead to extinction. Thereafter, we included in the model the fact that the level of equality in the community may be constantly changing under the influence of co-selection. This in turn leads to changes in average demographic characteristics and associated life-history traits. It is interesting that this model demonstrates a so-called demographic-economic paradox, which is traditionally considered to be the main empirical argument against the Malthus theory. In conclusion, we consider the anti-Malthus or pro-Condorcet model in which resources available to the community can grow at the same pace as the population. Despite the fact that such a community has always been unstable (has no equilibrium size or carrying capacity), it may nevertheless be limited and exist for a long time due to co-selection. Analysis of this model demonstrates a significant similarity in the results with the empirical model of demographic transition.

An attempt to unify some population growth models from first principles

Revista Brasileira de Ensino de Física, 2017

In this work, some phenomenological growth models based only on the population information (macroscopic level) are deduced in an intuitive way. These models, for instance Verhulst, Gompertz and Bertalanffy-Richards models, are introduced in such a way that all the parameters involved have a physical interpretation. A model based on the interaction (distance dependent) between the individuals (microscopic level) is also presented. This microscopic model have some phenomenological models as particular cases. In this approach, the Verhulst model represents the situation in which all the individuals interact in the same way, regardless of the distance between them (mean field approach). Other phenomenological models are retrieved from the microscopic model according to two quantities: i) the way that the interaction decays as a function the distance between two individuals and ii) the dimension of the spatial structure formed by the individuals of the population. This microscopic model ...

An economic-demographic dynamical system

Mathematical Modelling of Natural Phenomena

Human population growth has been called the biggest issue the humanity faces in the 21st century, and although this statement is globally true, locally, many Western economies have been experiencing population decline. Europe is in fact homeland for population decline. By 2050 many large European economies are predicted to lose large parts of their population. In this work, we consider the dynamical system that corresponds to the model introduced by Volpert et al. [Nonlinear Anal. 159 (2017) 408–423]. With the help of this model, we illustrate scenarios that can lead, in the long-run, to sharp population decline and/or deterioration of the economy. We also illustrate that even when under certain conditions the population will go extinct, temporarily it might experience growth.

On population growth with catastrophes

arXiv: Probability, 2020

Deterministic population growth models can exhibit a large variety of flows, ranging from algebraic, exponential to hyper-exponential (with finite time explosion). They describe the growth for the size (or mass) of some population as time goes by. Variants of such models are introduced allowing logarithmic, exp-algebraic or even doubly exponential growth. The possibility of immigration is also raised. An important feature of such growth models is to decide whether the ground state 0 is reflecting or absorbing and also whether state infinity is accessible or inaccessible. We then study a semi-stochastic catastrophe version of such models (also known as Piecewise-Deterministic-Markov Processes, in short, PDMP). Here, at some jump times, possibly governed by state-dependent rates, the size of the population shrinks by a random amount of its current size, an event possibly leading to instantaneous local (or total) extinction. A special separable shrinkage transition kernel is investigat...

The neoclassical model with variable population change

Proceedings of the 11th WSEAS international …, 2009

We extend the neoclassical growth model with logistic population change introduced by Ferrara and Guerrini [5] by considering a more general law for the population growth rate. In this kind of setup, the model is represented by a two dimensional dynamical system, whose non-trivial steady states, in contrast to the neoclassical model, may be node as well as saddle points.