A manner of characterizing the development of countries

Symbiosis Evolution Model and Behavior of Multiple Resource Agents in the Smart Elderly Care Service Ecosystem

Population aging has become an important factor restricting China′s social and economic development. The smart health and elderly care industry has developed rapidly in the past five years. However, the service resources among various elderly service providers are relatively isolated and scattered. In other words, the core management problem in the components of the smart elderly care service ecosystem is how to deal with the relationships of interest among multiple resource agents. Thus, the main contribution of this study is to employ symbiosis theory and the logistic growth model to construct a model of the evolution of the symbiosis of multiple resource agents in the smart elderly care service ecosystem. Then, we carry out a stability analysis, and analyze the evolutionary model of two resource agents′ symbiosis under different values of interdependence coefficients. Finally, we use computer simulations to dynamically simulate the model and comparatively analyze the population density of the hospital–nursing home symbiotic relationship using real cases in China. According to the study, we find that the enterprise goal in the smart elderly care service ecosystem should be to maximize the overall value of the multiple resource agents, and the result of the symbiotic evolution between different resource agents depends on the symbiotic interdependence coefficient, while the resource agent uses different strategies under different symbiosis models. Therefore, regulation is needed to ensure the relative fairness of the distribution of value co-creation in the smart elderly care service ecosystem when the resource agent takes actions that benefit itself. Of course, when the ecosystem is in a reciprocal symbiosis model, each resource agent benefits from the activities of the other resource agents, which is ideal in reality; in other words, the best symbiosis model between the two resource agents should be the similar reciprocal symbiosis model.

Transient and stationary characteristics of the Malthus-Verhulst-Bernoulli model with non-Gaussian fluctuating parameters

Two generalized Verhulst equations with non-Gaussian fluctuations of the reproduction rate and the volume of resources are under analytical investigation. For the first model, using the central limit theorem, we find the asymptotic behavior of the probability distribution of population density for an arbitrary non-Gaussian colored noise with nonzero power spectral density at zero frequency. Specifically, we confirm this result in the case of Markovian dichotomous noise and examine the evolution of mean population density. For fluctuating resources with one-sided stable distribution the transient dynamics of probability density function and statistical characteristics in the steady state are obtained. As shown, the scenario of the population's evolution depends on the parameter of nonlinearity in the original stochastic equation.

Social dynamics and the quantifying of social forces

SOCIAL AND INDUSTRIAL EVOLUTIONARY PROCESSES ARE CONSIDERED TO BE A SEQUENCE OF REPLACEMENTS OR SUBSTITUTIONS: new ideas for old, new labor patterns for old, new technologies for old. The logistic equation has often been used to describe population growth processes and replacement processes. It sometimes suffers from contradicting observational data. It is shown here that the deviations are often associated with unusual intermittent events-wars, strikes, economic panics, etc.-and that in many cases a few years after the event it can be abstracted as an instantaneous delta function impulse. After the event, the evolutionary process continues along its normal course. A formula is derived to use the observational data to determine the strength of the impulse modeling an event.

Exact probability distribution for the Bernoulli-Malthus-Verhulst model driven by a multiplicative colored noise

We report an exact result for the calculation of the probability distribution of the Bernoulli-Malthus-Verhulst model driven by a multiplicative colored noise. We study the conditions under which the probability distribution of the Malthus-Verhulst model can exhibit a transition from a unimodal to a bimodal distribution depending on the value of a critical parameter. Also we show that the mean value of x(t) in the latter model always approaches asymptotically the value 1.

Analysis of logistic growth models

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions.A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting.

A model of urbanization with nonlinear migration flows

"This paper seeks an appropriate specification of the migration exchange between rural and urban areas so that the implied evolution of the degree of urbanization agrees with its commonly observed S-shape. After demonstrating that the gross migration flows between rural and urban areas should be specified as nonlinear functions of the population in the origin sector, the paper introduces a model in which such flows are represented by gravity-type functional forms....[The model] can be used to give insights into the time paths of three basic urbanization variables: the urban-rural growth rate differential, the rural net outmigration rate, and the urban net immigration rate. All take on a zero value at the two extremes of the urbanization process and evolve in between according to a bell-shaped curve. These findings are illustrated by applying the model to data from the United States for the period 1790-1980."

A strategy for generating and testing models of migration and urban growth

"In this paper, it is argued that to identify the appropriate conditions under which the traditional gravity-type migration model should be tested, it is necessary to consider the wider demographic-economic framework in which such models play an essential part. The traditional model and attempts to make it more realistic in an ad hoc way are first sketched, and then the model is embedded in a dynamic framework based on nonlinear differential equations of the logistic kind describing the growth of population and employment. The role of the gravity model in coupling these equations is then developed." A theoretical analysis of this framework is then presented using simulation. "The simplest possible two-region case involving urban and rural regions is developed and after preliminary simulations, a more realistic version involving urban core, suburb and rural hinterland is proposed. A number of variants of this model are tested using simulation and it is concluded that in devising an appropriate test for this type of migration model, attention should be switched from spatial to temporal variation in migration using highly polarized spatial situations such as city regions." (summary in FRE, GER)