From behavioural to population level: Growth and competition

The aim of this work is to build models of population dynamics for growth and competition interaction by starting with detailed models at the individual level. At the individual level, we start with detailed models where the growth is described by linear terms. By considering individual interferences and by using aggregation methods, we show that the population level, different growth equation can emerge. We present an example of the emergence of logistic growth and an example of the emergence of logistic growth with Allee effect. Furthermore, in the case of two populations, we show that individual interferences can lead at the population level, to a model which has the same qualitative dynamics behaviour as the Lotka-Volterra competition model. Finally, we show that our model brings to light the effects of spatial heterogeneity on competition models. First, we find the stabilizing effects but also we show that destabilizing effects can occur.     

The Solow model improved through the logistic manpower growth law

In this paper the neo-classical economic Solow-Swan model (1956) has been improved replacing its Malthusian manpower law with the Verhulst (logistic) one. The relevant ordinary differential equation for the ratio capital/work has been then integrated in closed form via the Hypergeometric function₂ F ₁. The logistic growth injection for the manpower is detected to induce a more slow dynamics onto the Solow-Swan system, which keeps its stability. Increasing developments are displayed as the technologic progress rises. Further sceneries are tested and the congruence of the new solution with the classical one is shown switching to zero the selflimitation coefficent in the logistic law. Research supported by MURST grant:Metodi matematici in economia     

Waves analysis and spatiotemporal pattern formation of an ecosystem model

In this paper, we consider a predator–prey model given by a reaction–diffusion system. This model incorporates Holling-type-II (Michaelis–Menten) and modified Leslie-Gower functional responses. We show the existence of qualitatively different types of system behaviors realized for various parameter values. Our model is investigated with methods of the qualitative theory and the theory of bifurcations. We generalize the traveling waves existence method for populations dynamics with positive derivative densities, to the predator–prey system in which growth densities may change sign. Parallel to this is a discussion and an analysis of alternative model outcomes such as complex pattern formation and spatio-temporal chaos behavior.     

A MICRO‐LEVEL ‘CONSUMER APPROACH’ TO SPECIES POPULATION DYNAMICS

ABSTRACT. In this paper we develop a micro ecosystem model whose basic entities are representative organisms which behave as if maximizing their net offspring under constraints. Net offspring is increasing in prey biomass intake, declining in the loss of own biomass to predators and Allee's law applies. The organism's constraint reflects its perception of how scarce its own biomass and the biomass of its prey is. In the short‐run periods prices (scarcity indicators) coordinate and determine all biomass transactions and net offspring which directly translates into population growth functions. We are able to explicitly determine these growth functions for a simple food web when specific parametric net offspring functions are chosen in the micro‐level ecosystem model. For the case of a single species our model is shown to yield the well‐known Verhulst‐Pearl logistic growth function. With two species in predator‐prey relationship, we derive differential equations whose dynamics are completely characterized and turn out to be similar to the predator‐prey model with Michaelis‐Menten type functional response. With two species competing for a single resource we find that coexistence is a knife‐edge feature confirming Tschirhart's [2002] result in a different but related model.     

Dynamical approach to complex regional economic growth based on Keynesian model for China

The paper addresses the problem of complex regional economic growth by using nonlinear Keynesian model with focusing on direct foreign investments effects. We investigate the dynamics of the model for the broad range of parameters which, in particular, contains the parameter values obtained recently by econometric analysis of the data for economic growth in China. For the single-region model we give conditions for which the dynamics of the model will be chaotic or regular. The parameters which prevent the economic stagnation are indicated. Further, we consider the model for two regions with a common trade as a coupling factor. The conditions are given for the two trading systems to exhibit chaotic synchronization, in-phase and out-of-phase behavior.     

基于广义脉冲的东北三省外贸外资与经济增长研究

作为连接其他国家和地区的桥梁和纽带,对外经贸在国际经济关系中有着十分重要的地位。本研究选取对外经贸与经济增长代表性指标,以各指标平均增长率为切入点,通过构建相对增长指数模型,测算东北三省的外贸相对增长指数(TGI)和外资相对增长指数(CGI)并进行分类,结果显示三省外贸、外资增长类型截然不同。进一步,将历年外贸、外资增速与经济增速进行对比分析发现,外贸增速与经济增速具高度同步性,且始终扮演经济晴雨表的角色,外资增速则更具不确定性和偶然性。最后,广义脉冲响应分析显示外贸外资冲击经济增长均产生显著效应,但响应程度不尽相同,各指标贡献度通过方差分解呈现。本文为外贸外资与经济增长关系研究提供了新的视角。     

坑口电厂低碳经济发展系统动力学仿真研究

通过分析坑口电厂低碳经济系统的复杂结构特征和动态反馈机制,建立了坑口电厂低碳经济系统动力学模型,描述系统内部各要素之间的相互关系,并以平煤集团坑口电厂为例,对不同发展方案下的坑口电厂低碳经济系统进行仿真模拟.结果表明:科技投资、环保投资、能源利用率、能源消费结构等因素是影响坑口电厂低碳经济发展的关键因素;可以通过优化能源消费结构,提高煤矸石消耗比例;增加科技投资和环保投资,提高能源利用和转换效率,降低污染物和二氧化碳排放量,从而达到高效率、低能耗、低排放的低碳经济发展模式.     

Dynamics of a Stochastic SIR Epidemic Model with Logistic Growth

In this paper, a stochastic SIR epidemic model with saturated treatment function, non-monotone incidence rate and logistic growth is studied. First, we prove that the stochastic model has a unique global positive solution. Next, by constructing a suitable Lyapunov function, we can show that there exists an ergodic stationary distribution in the random SIR model. Then, we show that a sufficient condition can make the disease tend to extinction. Finally, some numerical simulations are used to prove our analytical result.     

Bifurcations in a predator–prey model with general logistic growth and exponential fading memory

A multiparameter predator–prey system generalizing the model introduced in [6] is considered. The system studied in this paper corresponds to the type of models with exponential fading memory where the logistic per capita rate growth of the prey is given by an arbitrary function of class C^k, k ≥ 3. We prove that the model has a Hopf bifurcation and that there exist open sets in the parameter space such that the system exhibits singular attractors and asymptotically stable limit cycles. A numerical simulation is conducted in order to show the existence of critical attractor elements.As pointed out by Ayala et al. in [14], the Lotka–Volterra model of interspecific competition, which is based on the logistic theory of population growth and assumes that the intra and interspecific competitive interactions between species are linear, does not explain satisfactorily the population dynamics of some species. This is due to fact that the model does not take into account some important features of the population, which affect its dynamics. The model introduced in this paper provides independent conditions of these facts, for the existence of a Hopf bifurcation and the asymptotically stable limit cycles.     

An Improved Solow—Swan Model

§1.　IntroductionThetheoryofeconomicgrowthisanimportanttopicinMacroeconomics.Afterador-mancynearlytwodecades,thestudyofeconomicgrowthbecamevigorousagaininthemid-1980s.TheSolow-Swanmodel[1]isoneofthemostusedinthisfield.Thismodelhasarousedmanyresearchersinterestintherecentyears.N.G.Manki,etal(1992)[2]appliedthismodeltoexaminewhetheritisconsistentwiththeinternationalvariationinthestandardofliving.W.Easterly(1993)[3]gavearevisedSolow-SwanmodelbyintroducingtheCESproductionfunction.Inthepaper…     

From a cellular automaton model of tumor–immune interactions to its macroscopic dynamical equation: A drift–diffusion data analysis approach

Several models of tumor growth have been developed from various perspectives and for multiple scales. Due to the complexity of interactions, how the macroscopic dynamics formed by such interactions at the microscopic level is a difficult problem. In this paper, we focus on reconstructing a model from the output of an experimental model. This is carried out by the data analysis approach. We simulate the growth process of tumor with immune competition by using cellular automata technique adapted from previous studies. We employ an analysis of data given by the simulation output to derive an evolution equation of macroscopic dynamics of tumor growth. In a numerical example we show that the dynamics of tumor at stationary state can be described by an Ornstein–Uhlenbeck process. We show further how the result can be linked to the stochastic Gompertz model.     

Monte Carlo scenario generation for retail loan portfolios

Monte Carlo simulation is a common method for studying the volatility of market traded instruments. It is less employed in retail lending, because of the inherent nonlinearities in consumer behaviour. In this paper, we use the approach of Dual-time Dynamics to separate loan performance dynamics into three components: a maturation function of months-on-books, an exogenous function of calendar date, and a quality function of vintage origination date. The exogenous function captures the impacts from the macroeconomic environment. Therefore, we want to generate scenarios for the possible futures of these environmental impacts. To generate such scenarios, we must go beyond the random walk methods most commonly applied in the analysis of market-traded instruments. Retail portfolios exhibit autocorrelation structure and variance growth with time that requires more complex modelling. This paper is aimed at practical application and describes work using ARMA and ARIMA models for scenario generation, rules for selecting the correct model form given the input data, and validation methods on the scenario generation. We find when the goal is capturing the future volatility via Monte Carlo scenario generation, that model selection does not follow the same rules as for forecasting. Consequently, tests more appropriate to reproducing volatility are proposed, which assure that distributions of scenarios have the proper statistical characteristics. These results are supported by studies of the variance growth properties of macroeconomic variables and theoretical calculations of the variance growth properties of various models. We also provide studies on historical data showing the impact of training length on model accuracy and the existence of differences between macroeconomic epochs.     

Existence of traveling waves to any Lax shock satisfying Oleinik’s criterion in conservation laws

Given any shock wave of a conservation law where the flux function may not be convex, we want to know whether it is admissible under the criterion of vanishing viscosity/capillarity effects. In this work, we show that if the shock satisfies the Oleinik’s criterion and the Lax shock inequalities, then for an arbitrary diffusion coefficient, we can always find suitable dispersion coefficients such that the diffusive-dispersive model admits traveling waves approximating the given shock. The paper develops the method of estimating attraction domain for traveling waves we have studied before.     

An allometric scaling relation based on logistic growth of cities

The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed “exponential allometry”, which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the above mentioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed “logistic allometry”. The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.     

资产组合,随机经济增长和政府政策的影响

本文在一个连续时间的经济增长模型中考虑政府政策、投资策略和个体福利 .在给定的生产技术 ,偏好和随机冲击的假设下 ,本文得到了持有资产税后期望回报、随机经济增长率、消费财富比、资产组合份额和各种资产实际回报率的显式解 .     

Two different routes to complex dynamics in an heterogeneous triopoly game

We study a triopoly game with heterogeneous players. The market is characterized by a nonlinear (isoelastic) demand function and three competitors. The main novelty is the double route to complex dynamics that we find and is quite rare in heterogeneous triopoly models. We show that the two routes have important implications for the economic interpretation of the dynamics emerging when the Cournot–Nash equilibrium becomes locally unstable. Moreover the model displays multistability of different attractors, requiring a global analysis of the dynamical system.     

关于Guzowska-Luís-Elaydi模型的分岔

本文考虑了一个离散的Logistic竞争模型.为了讨论分岔,给出了不动点的拓扑类型及非双曲的情况.应用中心流行约化定理,证明了跨临界分岔会在三个不动点上发生.本文还证明了在两个不动点处,跳跃分岔会发生,同时稳定的周期2轨会出现.     

具有生产性与福利性公共支出的随机内生增长模型

文章建立一个随机内生增长模型来阐明主要政策参数对经济增长与社会福利的影响.若对生产函数、效用函数、偏好及随机干扰作一些特殊的假设,我们证明了主要政策参数的均衡值能被模型参数唯一决定.进一步我们还得到了期望增长率与储蓄的清晰解.文章的最后,我们证明了政府支出直接影响个体决策者的决策:即提高经济增长率将减少福利;反之,增加福利将减少增长率.     

USING RESERVES TO PROTECT FISH AND WILDLIFE SIMPLIFIED MODELING APPROACHES

ABSTRACT. This paper investigates theoretically to what extent a nature reserve may protect a uniformly distributed population of fish or wildlife against negative effects of harvesting. Two objectives of this protection are considered: avoidance of population extinction and maintenance of population, at or above a given precautionary population level. The pre‐reserve population is assumed to follow the logistic growth law and two models for post‐reserve population dynamics are formulated and discussed. For Model A by assumption the logistic growth law with a common carrying capacity is valid also for the post‐reserve population growth. In Model B, it is assumed that each sub‐population has its own carrying capacity proportionate to its distribution area. For both models, migration from the high‐density area to the low‐density area is proportional to the density difference. For both models there are two possible outcomes, either a unique globally stable equilibrium, or extinction. The latter may occur when the exploitation effort is above a threshold that is derived explicitly for both models. However, when the migration rate is less than the growth rate both models imply that the reserve can be chosen so that extinction cannot occur. For the opposite case, when migration is large compared to natural growth, a reserve as the only management tool cannot assure survival of the population, but the specific way it increases critical effort is discussed.