Hopf bifurcation analysis in a multiple delayed innovation diffusion model with Holling II functional response

A nonlinear mathematical model with Holling II functional response describing the dynamics of nonadopter and adopters population in a stage structured innovation diffusion model, which incorporates the evaluation stage (multiple delays), is proposed. Firstly, we study the stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays at the positive equilibrium by analyzing the distribution of the roots of the corresponding exponential characteristic equation obtained through the variational matrix. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined with the help of normal form theory and center manifold theorem. Meanwhile, various cases are discussed to examine the effect of different delays on the stability of delayed innovation diffusion system and are also established numerically. It is also observed that the cumulative density of external influences has a significant role in developing maturity stage (adoption stage) in the system. Finally, numerical simulations are carried out to support and supplement the analytical findings.     

Stability and bifurcation analysis of a delayed innovation diffusion model

In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage(time delay) is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period(time delay, τ) passes through a critical value. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.     

Evaluating Web Services: Towards a framework for emergent contexts

The paper develops an evaluation framework with specific reference to Web Services. It is argued that the essential characteristics for such an approach, noted as qualitative, are captured in these constructs through an augmentation of theoretical considerations and empirical findings. A review of the innovation and diffusion literature indicates a considerable amount of research where attention is given to a range of features which may support Web Service adoption. It is argued that the framework proposed in this paper is of value in highlighting the specific situations for an effective evaluation in this respect.The empirical analysis was undertaken within five UK firms. Each of these organizations represent different business sectors including, Telecommunication (two firms), Independent Software Package Vendor (ISV), Software Engineering and Food Services industries. The study involved a cross-section organizational case approach within each situation for factors affecting adoption. The evidence suggests that the empirical data complements traditional innovation and diffusion theories. However, emergent context is identified as a significant influence on potential web evaluation processes to ensure appropriate investment targeting. The findings are noted to guide analysts in determining critical aspects of the complex issues involved and present suggestions for further valid research.     

多元技术创新扩散的系统动力学模型及仿真

本文力图放宽模型的假设,考虑创新技术市场间的非独立性、扩散过程中潜在采用-等待采用-已采用三阶段中时间延迟性,建立多元技术创新扩散的系统动力学模型,并用Vensim进行模拟仿真研究.仿真结果表明该模型比较符合实际,可为多元技术创新扩散的理论研究和实际实施提供理论指导.     

基于演化博弈的制造企业服务创新扩散研究

制造企业服务化是我国实现制造强国的必经之路,本文以“中国制造2025”战略为背景,通过借鉴创新扩散和演化博弈理论,对社会系统中参与服务创新的相关主体进行分析,构建政府与企业之间演化博弈模型,结合并改进Bass经典创新扩散模型,探究政府规制行为对企业服务创新行为演化及扩散的影响,利用Matlab对复制动态方程和扩散模型进行数学推导和数值仿真分析。结果表明:当满足政府的社会总收益大于其调控成本和各项补贴总额且企业选择服务创新策略时收益的额外增加额大于其实际投入时,系统才会演化至政府调控且企业采纳服务创新的稳定状态;适当增加政府对企业的调控力度、投入补贴和税收补贴有助于推进服务创新在系统中的扩散,其中税收补贴的感知能力最强,投入补贴最弱;将抑制系数引入Bass创新扩散模型,构建互补型、竞争型和替代型三种服务创新的扩散模式,其中竞争型扩散符合中国现阶段市场规律,替代性扩散将成为未来制造企业的发展趋势。     

A Singular Perturbation Analysis for a Reaction-Diffusion System Describing Pattern Formation

A reaction-diffusion system describing a simple activator-inhibitor reaction is investigated in the limiting case of “very large” diffusion rate of the inhibitor. Using singular perturbation techniques, an inner and an outer expansion are derived. The latter, describing the large-time behavior of the system, is governed by equations that, in the first orders of approximation, possess asymptotically stable space-inhomogeneous equilibria (patterns), and whose set of equilibria is globally attractive.     

应急不完全信息环境下的混合多属性协同决策方法

科学的应急救援协同决策理论方法,不但能使应急管理系统更好地发挥作用,而且能使政府及公众的应急救援行为更加规范和有序.为此,针对应急环境下决策信息不完全的背景,研究构建了一类综合集成网络层次分析法(ANP)、证据理论(D-SEvidence Theory)以及改进的理想点法(TOPSIS)的混合多属性应急协同决策方法.其中ANP用于处理应急救援方案非独立和相互联系的评价指标权重的确立,D-S Theory用于处理不完全信息条件下多个部门对应急救援候选方案的不同评价信息融合,改进的理想点法(TOPSIS)则用于最终候选应急救援方案的排序.研究结果表明,所提出的混合多属性协同决策方法不仅在理论上有所集成创新,而且在实际应用中可以有效解决应急环境下多部门或多环节协同决策问题.     

面向集群创新网络异质企业的知识扩散建模及仿真研究

基于合作的集群创新网络知识扩散已经成为企业实现知识创新的重要手段,而集群创新网络知识扩散的动力学过程强烈依赖于异质企业间知识扩散能力的影响,为此,本文综合考虑了企业间不同接触数量、知识吸收和传播能力、知识淘汰率等异质性因素,建立了基于传染病理论的知识扩散模型,验证了由各异质因素构成的知识扩散再生数对知识扩散均衡和扩散效果的影响,并结合仿真实验进一步得出:在知识扩散前期,集群创新网络应发挥hub节点及异质网络的优势加快知识扩散,在中后期应注意企业关系发展的均衡性及企业接触邻居的规模性;相比过于强调知识交流的广泛性,加强企业传播能力和吸收能力的培养对网络知识扩散效果的提升更具意义;随着时间演化,企业知识淘汰率也会影响网络知识扩散的收敛情况。     

Monotone scheme for finite difference equations concerning steady-state prey-predator interactions

In this article a system of semilinear elliptic partial differential equations is studied. This system determines the equilibria of the Volterra-Lotka equations describing prey-predator interactions with diffusion. To analyze the system, a new monotone scheme is presented. A rigorous foundation is given for numerical calculations by adapting a suitable finite difference method to the new monotone scheme. Earlier theories in finite differences are not successful in solving the system without this scheme.     

负面口碑、社会互动与创新扩散:基于小世界网络的仿真

为探究创新扩散失败的原因及作用机理,在创新扩散微观模型中引入负面口碑,建立个体在社会互动影响下的决策模型,并进行小世界网络中的多智能体仿真分析,研究网络结构、抵抗领袖比例、意见领袖创新性和社会规范约束力对创新扩散的影响。结果表明,考虑负面口碑的创新扩散曲线呈“S”形变化,但扩散深度受限;高度聚集的社会网络更有利于创新扩散。抵抗领袖比例越高,创新扩散速度和深度越小,且负面口碑作用范围越大;当抵抗领袖比例高于意见领袖比例时则会导致扩散失败。意见领袖创新性的提高可以缓解负面口碑的消极影响并促进创新扩散。社会规范约束力对创新扩散深度的影响随网络结构变化呈现不同态势。研究不但丰富了现有创新扩散理论,而且对开发创新推广策略具有指导意义。     

Time delayed parabolic system in a two-species competitive model with stage structure

A two-species competitive model with stage structure is discussed. The dynamics of coupled system of semilinear parabolic equations with time delays are investigated. Results on the local and global stabilities of the axial equilibria and positive equilibrium are given. Our results show that the introduction of diffusion does not affect the permanence and extinction of the species though the introduction of stage structure brings negative effect on it.     

网络结构、采纳者偏好与创新扩散:基于采纳者决策过程的创新扩散系统动力学模型仿真分析

在对采纳者决策过程分析的基础上,将网络结构和采纳者偏好作为核心参数,构建基于采纳者决策过程的创新扩散系统动力学模型。对模型进行仿真发现,在采纳者趋同化偏好条件下,网络平均度、网络重连概率与采纳者偏好强度的变动趋势与创新扩散效率的变动趋势相同,而在采纳者差异化偏好条件下则与创新扩散效率变动趋势相反。网络平均路径长度对创新扩散的影响方向与采纳者偏好特征无关,提高网络平均路径长度会始终降低创新扩散的效率。采纳者的趋同化偏好能够放大创新扩散对网络结构变量与采纳者偏好强度变量的敏感程度,采纳者差异化偏好则会缩小创新扩散对网络结构变量与采纳者偏好强度变量的敏感程度。研究结果对于制定创新推广策略具有一定的指导意义。     

IMPACT OF OPERATING COSTS ON INVESTMENT STRATEGIES IN NEW TECHNOLOGY ADOPTION WITH A FURTHER NEW TECHNOLOGY ANTICIPATED

The adoption of new technologies often represents a crucial component of firms＇ investment decisions. This paper studies a dynamic duopoly model in which two firms compete in adoption of current technology with a further new technology anticipated. Here it is assumed that the operating costs are not zero which has more explanatory power of the real world. There exist three kinds of equilibria that may occur in adoption of current technology, which mainly depends on the level of operating costs and the first-move advantage. It shows that the faster technological substitution or innovation encourages the leader to invest earlier while induces the follower to invest later. Furthermore,like the investment costs,with the increase of operating costs the follower tends to invest later while the leader tends to invest earlier ,the investment thresholds are more sensitive to the change of operating costs than that of investment costs.     

预期更新技术出现时新技术采用中经营成本对投资策略的影响

The adoption of new technologies often represents acrucial component of firms' investment decisions.This paper studies a dynamic duopoly model in which two firms compete in adoption of current technology with afurther new technology anticipated.Here it is assumed that the operating costs are not zero which has more explanatory power of the real world.There exist three kinds of equilibria that may occur in adoption of current technology,which mainly depends on the level of operating costs and the first-move advantage.It shows that the faster technological substitution or innovation encourages the leader to invest earlier while induces the follower to invest later.Furthermore,like the investment costs,with the increase of operating costs the follower tends to invest later while the leader tends to invest earlier,the investment thresholds are more sensitive to the change of operating costs than that of investment costs.     

考虑决策者失望规避的供应链协同绿色创新动态优化与协调研究

针对决策者存在失望规避行为且产品绿色水平具有动态变化特征的情形,基于失望理论,运用微分博弈的方法研究了供应链协同绿色创新动态优化与协调问题,探讨了供应链成员失望规避程度对绿色创新决策及供应链绩效的影响,并提出双向成本分担契约对供应链进行协调。结果表明,供应链成员是否选择协同绿色创新及产品的绿色水平均与成员的失望规避程度密切相关;分散式决策下,若制造商选择分担供应商部分绿色创新成本,其分担比例与制造商失望规避程度负相关,与供应商失望规避程度正相关;集中式决策下,产品绿色水平、成员绿色创新水平及效用现值均高于协调前分散系统中的对应值;在一定条件下,双向成本分担契约的设计与实施,能有效提升供应链成员效用现值,实现供应链协调。     

A revised Inno-Qual performance system for higher education: the integrated applications of DEMATEL and ANP

The Taiwanese higher education system has historically been a sustainable resource, providing a competitive advantage for Taiwan. However, its performance has recently decreased relative to other countries. Improving innovation and total quality management (TQM) performance has become important to increase the competitive advantage and survival rate of universities. The Inno-Qual performance system (IQPS) is the latest model to evaluate innovation and TQM performance in Taiwanese institutions of higher education. The IQPS not only addresses major technical problems that could damage the reliability of evaluation outcomes, but it also stresses that half of the universities have not efficiently improved their innovation and TQM performance simultaneously. However, criteria and weights for innovation and TQM dimensions of the IQPS are separated to consider internal and external organizational performance independently. This results in inconsistency between the weights, resulting in lack of a clear direction for making improvements, which makes the performance evaluation results impossible to confirm. Furthermore, the innovation weights ignore the effects of the TQM dimensions due to the separation, making the system irrational and invalid in the real world. The purpose of this study is to revise the current IQPS and overcome these two drawbacks by using the decision-making trial and evaluation laboratory application and the analytic network process. With a method that is efficient, less costly, and provides verifiable results, our revised IQPS can help improve innovation and TQM performance in today's universities.     

The stability of a diffusion model of plankton allelopathy with spatio–temporal delays

A reaction–diffusion system with non-local delay is proposed to describe two competitive planktonic growths in aquatic ecology. The local and global stability of the axial equilibria as well as the positive equilibrium are discussed. Our results show that the delay has no effect on the stability of the axial equilibria; on the other hand, the positive equilibrium can be induced to be locally unstable by the delay. Finally, the corresponding numerical simulations are also demonstrated.     

A time delay model for the diffusion of a new technology

In this paper, we propose a mathematical model with time delay to describe the process of diffusion of a new technology. This model is suitable for modeling diffusion processes of all those technologies that require great initial investments and public subsidies, such as technologies used for producing renewable energy. We consider external factors, such as the government policy and the production costs, that influence the decision of adoption of the new technology. We also consider the internal influence from adopters. The adoption process is described by a delay differential equation. The time delay represents the evaluation stage at which the potential consumers decide whether to adopt the new technology or not. A qualitative analysis is carried out in order to assess the stability of the equilibrium for certain parameters and to find the final level of adopters.     

THE EFFECT OF A PREDATOR RESOURCE ON A DIFFUSIVE PREDATOR PREY SYSTEM

A model of a predator-prey system with diffusion and predator resource is studied. Both constant and variable resources are considered. In the absence of diffusion, criteria for local stability, instability, and global stability of equilibria, as well as persistence and extinction, are obtained. It is shown that an otherwise unstable uniform equilibrium state may be stabilized by diffusion.     

Diffusion effect and stability analysis of a predator-prey system described by a delayed reaction-diffusion equations

In this paper, we consider a delayed reaction-diffusion equations which describes a two-species predator-prey system with diffusion terms and stage structure. By using the linearization method and the method of upper and lower solutions, we study the local and global stability of the constant equilibria, respectively. The results show that the free diffusion of the delayed reaction-diffusion equations has no effect on the populations when the diffusion is too slow; otherwise, the free diffusion has a certain influence on the populations, however, the influence can be eliminated by improving the parameters to satisfy some suitable conditions.