创新企业种群成长动力学分析

以生物系统中种群动力学为主要理论依据,开发了创新种群成长动力学模型.方程组推导结果表明:创新种群的成长过程中存在一定的均衡条件.科研种群是创新创群的主要互动种群.创新种群和科研种群之间存在显著地激励机制,两类种群对创新资源的占用存在一定的比例关系.创新种群的增长收到多种环境因素的影响,政府部门、服务机构、科研种群的影响均不同.创新种群的总量平衡点受总体环境制约.创新种群的增量平衡点主要受科研种群影响.     

考虑环境污染的随机经济增长模型

本文主要考虑了环境污染对个体福利的负面效应,把环境污染水平纳入效用函数,由此建立了一个随机经济增长模型.分析了经济均衡时税收,政府环保投资,私人环保投资对经济增长率和社会福利的影响.同时还求出了最优的增长率和个人资本与财富比,消费和财富比.     

一类具有Beddington-Deangelis功能反应捕食系统的收获模型

研究了一类具有Beddington-Deangelis功能反应捕食系统的收获模型,讨论该系统生物经济平衡点的性态,得到了系统正平衡点全局渐进稳定的充分条件;然后利用Pontryagin最大值原理得到了最优收获策略,讨论了贴现率能影响收获种群的利润水平.     

人力资本投资的随机内生增长模型

本文假设人力资本是宏观经济的一部分 ,由此建立一个随机内生增长模型 ,把人力资本作为宏观经济变量并进入个人效用 .分析了经济达到均衡时个体偏好 ,不确定性对均衡增长率的影响 .同时分析了财政政策 ,税率对经济增长的影响 ,还求出了最优的增长率和人力资本投入与物质资本比 .     

一个基于Keeping Up with the Joneses的随机内生增长模型

本文建立了一个基于Keeping up with the Joneses的随机内生增长模型,利用"伪双状态变量"法得到了均衡时的最优消费、最优经济增长率和最优福利,讨论了相对消费对它们的影响.     

Logistic种群演化模型的渐近加权周期性

在生态动力学研究中,研究者们往往假设环境因素f(t)随着季节变化而发生周期性变化.但是诸如光照等因素在这-年的变化都将有别于上-年.因此环境的变化不是严格周期的,从而f(t+T)=w(t)f(t),这里的w(t)≠1.在我们前期工作中称这类函数为加权周期函数.本文针对Logistic种群演化模型研究了这-情况,得到了-个有趣的结果:当内禀增长率和种内竞争率都发生加权周期变化时,种群演化会呈现出某种渐近加权周期性,而且其权函数刚好是种内竞争率权函数的倒数.这很好地解释了-个生态学现象:种内竞争加剧则意味着种群数量加快下降.     

两种群竞争和合作模型的全局渐近稳定性

其中R=r/K,r为种群的内禀自然增长率,K为环境容纳量,N为种群数量(或密度)。 考虑在周期环境中两种群竞争(合作),此时每一种群的生长由于另一种群的存在而减少(增加),可设这时i种群的环境容纳量为     

人力资本、自然资本与最优经济增长要素分析

通过把人力资本、自然资本与社会生产总量联系起来 ,由消费物资多少、获得知识多少及自然资本存量大小这三因素来确定效用 ,提供了物质、人力和自然资本三种重要资产增长的模型框架 ,得到了经济的消费增长率、均衡时各种资本的增长率之间的关系和实现最优经济增长的控制策略 .     

基于生灭过程的多斑块毒杂草入侵模型及空间模拟

本文将生灭过程模型应用到多斑块毒杂草入侵问题中,研究毒杂草与周围有限数量斑块的可食牧草之间的入侵关系.借助生灭过程理论,利用全期望公式构建微分方程,计算出毒杂草的期望值.通过讨论极限期望,分析得出毒杂草成功入侵至周围斑块的条件.采用元胞自动机理论将入侵模型扩展到空间网格进行模拟研究,分析毒杂草属的空间分布类型,为毒杂草的控制提供数据支持.研究结果表明:(1)若毒杂草的内禀增长率大于死亡率且内禀增长率和死亡率之差大于毒杂草的入侵率时,毒杂草成功入侵至可食牧草的概率变大,增加了可食牧草灭绝的风险,不利于可食牧草的续存;(2)若毒杂草的内禀增长率小于死亡率或内禀增长率和死亡率之差小于毒杂草的入侵率时,毒杂草没有足够的生物量向可食牧草入侵,毒杂草成功入侵至可食牧草的概率变小;(3)毒杂草的入侵作用影响了毒杂草种群的空间分布特征,加快了空间分布的聚集程度.     

时间不一致偏好、污染治理与经济增长

本文在考虑污染治理的内生经济增长模型中引入时间不一致偏好,得到市场均衡的最优消费、最优污染治理投入和经济增长率,研究时间不一致偏好和污染对消费、污染治理投入、经济增长和福利成本的影响.本文研究发现时间不一致偏好会降低消费和污染治理投入,提高经济增长率和降低福利成本.污染的负生产效应越大,污染治理投入越多,消费、经济增长率越低,而福利成本越高.污染负效用参数和个体感受程度的影响是不确定的.     

基于模糊综合评价模型的赣州市水资源承载力动态评价

水资源的合理利用对区域经济社会发展以及促进人与自然的可持续发展至关重要.通过构建模糊综合评价模型,选取年降水量、人均水资源量、水资源利用率、万元GDP用水量、万元工业增加值用水量、农田灌溉亩均用水量、生态用水等7个指标对赣州市2009-2018年水资源承载力进行动态评价研究,分析近十年该地区水资源承载力演变趋势以及影响该地区水资源承载力的主要因素.结果表明:1)赣州市水资源综合承载力较高,水资源还有进一步开发利用的空间;2)2009-2018年赣州市水资源承载力整体上呈上升趋势,但上升幅度不大,呈现小幅波动状态,其中GDP、工业用水量以及农业用水量对赣州市水资源承载力的具有显著影响;3)赣州市水资源较丰富,但由于时空分配不均,水资源配置体系也不够完善,且供水的基础设施比较薄弱,所以水资源的开发利用程度比较低.该研究结果可为当地水资源的可持续利用提供决策参考和依据.     

Optimal impulsive harvesting on non-autonomous Beverton–Holt difference equations

Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting.     

Optimal impulsive harvesting on non-autonomous Beverton–Holt difference equations

Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting.     

周期Gompertz生态系统中的最优脉冲控制收获策略

以周期Gompertz系统为基础,讨论了周期变化的单种群生物资源的收获优化问题及种群的动力学性质.在单位收获努力量假设下,以最大可持续收获量为管理目标,确定了线性收获下的最优收获策略,获得了最优收获努力量、最大可持续收获及相应的最优种群水平的显示表达式,为自然资源的开发和利用提供了理论依据.     

OPTIMAL IMPULSIVE CONTROL IN COMPETITIVE SYSTEM

In this paper,the impulsive exploitation of two species periodic competitive system is considered.First,we show that this type of system with impulsive har- vesting has a unique positive periodic solution,which is globally asymptotically stable.Further,by choosing the maximum total revenues as the management objective,we investigate the optimal harvesting policies for periodic competi- tive system with impulsive harvesting.Finally,we obtain the optimal time to harvest and optimal population level.     

广义Richards-Gilpin-Ayala模型的捕获优化问题

在Richards-Gilpin-Ayala模型的基础上,提出了一类更广泛的数学模型—广义Richards-Gilpin-Ayala模型.进而讨论该模型单种群生物资源的捕获优化问题,分析了被开发生物种群的动力学性质.在单位捕获努力量假定下,以最大可持续捕获量为管理目标,确定了线性捕获下的最优捕获策略,得到了最优捕获努力量,最大可持续收获及相应的最优种群水平的显式表达式.这些结果推广了相关文献中关于Schaefer模型、广义Logistic模型的相应结果.     

一类半线性时变种群系统的最优捕获控制

讨论了年龄相关的半线性时变种群系统的最优捕获控制问题.根据微积分方程及泛函分析的知识证明了最优捕获控制的存在性,得到了捕获控制为最优的必要条件.     

Optimal harvesting policy for stochastic Logistic population model

In this paper, we consider some optimal harvesting policies for single population models, in which the harvest effort and the intrinsic growth rate are disturbed by environment noises. We choose the maximum sustainable yield and the maximum retained profits as two management objectives, and obtain the optimal harvesting policies, respectively. For the two objectives, we give the optimal harvest effort that maximizes the sustainable yield (or retained profits), the maximum of expectation of sustainable yield (or retained profits) and the corresponding variance. Their explicit expressions are determined by the coefficients of equation and the disturbance intensity.     

ON THE RELATIONSHIPS BETWEEN NATURAL AND HARVEST MORTALITIES OF THE MALLARD

A discrete optimal control approach is used to show that the intensity of harvest of mallard populations in North America, at steady state, is sensitive to the strength of compensation between natural mortality and harvest mortality. Optimal harvest is less sensitive to changes in the natural mortality rate than to the interaction between natural and harvest mortalities. The management implications are: (1) if compensatory mortality operates, then more animals may be harvested without endangering the population, and (2) managers should pay particular attention to this mechanism in studying population dynamics.     

Impacts of two-stage deterioration on an integrated inventory model under trade credit and variable capacity utilization

The joint economic lot sizing problem (JELP) model provides a global view to facilitate the development of a production-inventory policy for an integrated system. However, when a deteriorating item is involved, previous studies have neglected the following two important issues: (1) the deterioration quantity increases the demand for the supplier's capacity, which consequently requires the supplier to recalculate the corresponding average cost and reevaluate the capacity utilization, and (2) given the supplier's production rate, in-transit deterioration imposes restrictions on the delivery distance or in-transit time. Therefore, the existing integrated policies may lead to infeasible solutions for the distribution channel when a deterioration item is included. In view of these two issues, a generalized JELP model under delay in payments is formulated to investigate the integrated production-inventory policy for an item with two-stage deterioration (in-transit and retail deterioration) while incorporating both transportation time and capacity utilization. By developing the average cost functions of the supply chain members and employing several new definitions (e.g., variable capacity utilization), this paper provides a mechanism for measuring the influence of two-stage deterioration on the supplier's capacity utilization for the JELP. Three algorithms are proposed to obtain optimal decisions based on the theoretical results. This paper demonstrates that the supplier's variable capacity utilization is relevant to transportation time and two-stage deterioration, which can be applied to evaluate the feasibility of the integrated production-inventory policy for the deteriorating item. Furthermore, there is a maximum allowable value for the retailer's order cycle.