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.     

Innovation diffusion: Some new technological substitution models

Three innovation diffusion models of technology (KKKI‐KKKIII) are proposed. The first two of these models are motivated by Smith's model and von Bertalanffy's model already in use in population dynamics. The first model also takes into account the internal and external influences of imitators and innovators. The third model is an improvement over models by Floyd and Fisher‐Pry. It can also be looked upon as a model which takes into account the effect of promotional subsidies on the innovation diffusion. Empirical analyses using the data of three technological innovations show that the proposed models give comparable or better results.     

考虑IT基础设施作用的外部知识对企业流程创新影响的博弈模型

本文基于知识基础观理论和吸收能力理论,以两个异质性制造企业组成的寡头竞争市场为研究对象,参考经典研发竞争AJ模型和非对称研发模型,建立考虑IT基础设施作用的外部知识对企业流程创新影响的博弈模型。研究表明,对于异质性企业来说,成本和IT基础设施投入占优的企业通过流程创新将拥有更大的市场份额,且企业通过合作创新方式引入的外部知识量也随着初始生产成本差异和IT基础设施投入的变化而改变,总体来说,企业异质性是企业流程创新竞争不平衡性的重要原因。考虑IT基础设施作用的情况下,企业引入外部知识进行流程创新对均衡产量具有正向影响,对均衡利润的影响存在阈值,呈现先增加后降低的趋势。由于溢出效应的存在,两个企业的均衡利润随领先企业的IT基础设施投入的增加而增加,但领先企业的均衡利润随IT基础设施投入的增加幅度更大,且领先企业的均衡利润占优。本文进一步提出了加强IT基础设施建设,促进外部知识利用,提升企业流程创新能力的管理启示。     

Similarity solution for a cylindrical shock wave in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux

The propagation of shock waves in a rotational axisymmetric dusty gas with heat conduction and radiation heat flux, which has a variable azimuthally fluid velocity together with a variable axial fluid velocity, is investigated. The dusty gas is assumed to be a mixture of non-ideal (or perfect) gas and small solid particles, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston (or inner expanding surface). The fluid velocities in the ambient medium are assume to be vary and obey power laws. The density of the ambient medium is assumed to be constant, the heat conduction is express in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient α_R are assumed to vary with temperature and density. In order to obtain the similarity solutions the angular velocity of the ambient medium is assume to be decreasing as the distance from the axis increases. The effects of the variation of the heat transfer parameter and non-idealness of the gas in the mixture are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also investigated.     

A feedback nash equilibrium solution for non–cooperative innovations in a stochastic differential game framework

In this paper, a stochastic model of non–cooperative technological innovations is developed. A feedback Sash equilibrium solution is obtained and the equilibrium innovation strategies are derived in explicit form. Several interesting properties of the equilibrium strategies are observed. On the one hand, an increase in the degree of competition in the industry, in the discount rate or in the state of technologyreduces innovation efforts. On the other hand, an increases the rate of degradation of the state of technology due to obsolescence results in an increase in innovation investment. While an increase in uncertainty reduces the expected present value of present and future discounted profits innovation efforts increase as uncertainty increases     

The fractional-order SIS epidemic model with variable population size

In this work, we deal with the fractional-order SIS epidemic model with constant recruitment rate, mass action incidence and variable population size. The stability of equilibrium points is studied. Numerical solutions of this model are given. Numerical simulations have been used to verify the theoretical analysis.     

Estimating conjectural variations for electricity market models

Agents’ behavior in oligopolistic markets has traditionally been represented by equilibrium models. Recently, several approaches based on conjectural variations equilibrium models have been proposed for representing agents’ behavior in electrical power markets. These models provide insight of market equilibrium sensitivity to agents’ strategies and external variables, and therefore, they are widely applied. Unfortunately, not enough analysis has been done in how these user-supplied parameters, the conjectural variations, should be estimated. This paper proposes a parameter inference procedure based on two stages. The first stage infers historical values of the parameter by fitting the models’ results to historical market data. The second stage is based on a statistical time-series model whose objective is to forecast parameter values in future scenarios. Additionally, results of this procedure’s application to a real-size case are presented.     

高技术产业创新种群的种内关系结构对其创新输出能力的影响

技术创新是多样化的异质性个体企业在一定时空范围内互动作用下涌现出的系统性输出结果.基于动态面板系统GMM模型,利用2009-2018年的省际数据对中国高技术产业创新生态系统中创新种群的种内关系结构与种群创新输出功能的互动影响关系进行研究.研究结果表明:第一,技术创新种群的种群规模尚未达到对外部环境容纳量的理想水平.第二...     

An oligopoly model of dynamic advertising competition

An oligopoly model is presented that allows the determination of feedback Nash equilibrium advertising strategies for an oligopoly. Analyses of symmetric and asymmetric oligopolies with the model show that unit contribution and advertising effectiveness have positive effects on a competitor’s own advertising and steady-state sales, while discount rate and decay rate have negative effects. An asymmetric analysis further shows that unit contribution and advertising effectiveness affect positively, and discount rate and decay rate negatively, a competitor’s rivals’ advertising, but have effects in opposite directions regarding rivals’ steady-state sales. The symmetric and asymmetric analyses also show that steady-state sales per competitor decline with the number of competitors in the oligopoly, while total oligopoly steady-state sales increase. The model is applied empirically to the triopolistic competition involving Anheuser-Busch, SABMiller, and Molson Coors in the beer industry.     

Diffusion dynamics in small-world networks with heterogeneous consumers

Diffusions of new products and technologies through social networks can be formalized as spreading of infectious diseases. However, while epidemiological models describe infection in terms of transmissibility, we propose a diffusion model that explicitly includes consumer decision-making affected by social influences and word-of-mouth processes. In our agent-based model consumers’ probability of adoption depends on the external marketing effort and on the internal influence that each consumer perceives in his/her personal networks. Maintaining a given marketing effort and assuming its effect on the probability of adoption as linear, we can study how social processes affect diffusion dynamics and how the speed of the diffusion depends on the network structure and on consumer heterogeneity. First, we show that the speed of diffusion changes with the degree of randomness in the network. In markets with high social influence and in which consumers have a sufficiently large local network, the speed is low in regular networks, it increases in small-world networks and, contrarily to what epidemic models suggest, it becomes very low again in random networks. Second, we show that heterogeneity helps the diffusion. Ceteris paribus and varying the degree of heterogeneity in the population of agents simulation results show that the more heterogeneous the population, the faster the speed of the diffusion. These results can contribute to the development of marketing strategies for the launch and the dissemination of new products and technologies, especially in turbulent and fashionable markets. This paper won the best student paper award at the North American Association for Computational Social and Organizational Science (NAACSOS) Conference 2005, University of Notre Dame, South Bend, Indiana, USA. Preceding versions of this paper have been presented to the Conference of the North American Association for Computational Social and Organizational Science (NAACSOS), 2005, University of Notre Dame, South Bend, USA and to the Conference of the European Social Simulation Association (ESSA), 2005, Koblenz, Germany. Sebastiano Alessio Delre received his Master Degree in Communication Science at the University of Salerno. After one year collaboration at the Institute of Science and Technologies of Cognition (ISTC, Rome, Italy), now he is a PhD student at the faculty of economics, University of Groningen, the Netherlands. His work focus on how different network structures affect market dynamics. His current application domain concerns Agent-Based Simulation Models for social and economic phenomena like innovation diffusion, fashions and turbulent market. Wander Jager is an associate professor of marketing at the University of Groningen. He studied social psychology and obtained his PhD in the behavioral and social sciences, based on a dissertation about the computer modeling of consumer behaviors in situations of common resource use. His present research is about consumer decision making, innovation diffusion, market dynamics, crowd behavior, stock-market dynamics and opinion dynamics. In his work he combines methods of computer simulation and empirical surveys. He is involved in the management committee of the European Social Simulation Association (ESSA). Marco Janssen is an assistant professor in the School of Human Evolution and Social Change and in the Department of Computer Science and Engineering at Arizona State University. He got his degrees in Operations Research and Applied Mathematics. During the last 15 years, he uses computational tools to study social phenomena, especially human-environmental interactions. His present research focuses on diffusion dynamics, institutional innovation and robustness of social-ecological systems. He combined computational studies with laboratory and field experiments, case study analysis and archeological data. He is an associate editor-in-chief of the journal Ecology and Society.     

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.     

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。     

Modeling Reputational and Informational Influences in Threshold Models of Bandwagon Innovation Diffusion

Bandwagon innovation diffusion is characterized by a positive feedback loop where adoptions by some actors increase the pressure to adopt for other actors. In particular, when gains from an innovation are difficult to quantify, such as implementing quality circles or downsizing practices, diffusion is likely to occur through a bandwagon process. In this paper we extend Abrahamson and Rosenkopf&2018;s (1993) model of bandwagon diffusion to examine both reputational and informational influences on this process. We find that the distribution of reputations among the set of potential adopters affects the extent of bandwagon diffusion under conditions of moderate ambiguity, and we find that bandwagons occur even when potential adopters receive information about others&2018; unprofitable experiences with the innovation.     

Diffusion and growth in an evolving network

We study a simple model of a population of agents whose interaction network co-evolves with knowledge diffusion and accumulation. Diffusion takes place along the current network and, reciprocally, network formation depends on the knowledge profile. Diffusion makes neighboring agents tend to display similar knowledge levels. On the other hand, similarity in knowledge favors network formation. The cumulative nonlinear effects induced by this interplay produce sharp transitions, equilibrium co-existence, and hysteresis, which sheds some light on why multiplicity of outcomes and segmentation in performance may persist resiliently over time in knowledge-based processes.     

基于生产结构视角的高新技术产业技术扩散影响研究

基于奥地利学派生产结构视角探讨高新技术产业外部技术扩散的影响路径,提出技术扩散通过生产结构的迂回性作用于技术创新,进而影响产出绩效。基于2005~2014年我国四个高新技术产业的面板数据,利用stata14软件进行数据分析,并对所提假设进行检验。结果表明:外部技术扩散对生产结构迂回性具有正向影响,但迂回性负向影响企业技术自主创新能力。研究结论对企业提升产业竞争力、增强技术创新和创新扩散效率具有重要的理论和实践启示。     

两类出生带有密度制约的不育控制下的害鼠模型

建立了两类出生带有密度制约的不育控制下的害鼠模型,利用Hurwitz判据,证明了平衡点的局部渐近稳定性,对全局稳定性进行了数值模拟,讨论了主要参数对种群动态变化的影响.     

Cooperative advertising in a distribution channel with fairness concerns

Cooperative (co-op) advertising has been widely used in practice and employed as a strategy to improve the performance of a distribution channel. It is known from the existing models that co-op advertising could not achieve the channel coordination (i.e., maximize the total channel profit). In this paper, we consider a distribution channel consisting of a single manufacturer and a single retailer, and investigate the effect of the retailer’s fairness concerns. Applying the equilibrium analysis, we obtain the following results: (1) Channel coordination can be achieved if the retailer has fairness concerns and model parameters satisfy certain conditions. (2) Although both channel members become better off with co-op advertising if neither channel member has fairness concerns, we find situations where co-op advertising brings detrimental effects to the retailer if the retailer has fairness concerns. (3) The retailer’s fairness concerns may increase or decrease the equilibrium participation rate, the equilibrium advertising effort, and the equilibrium profit of the manufacturer and the whole channel. (4) We identify the conditions under which the effectiveness of co-op advertising can be improved or reduced by the retailer’s fairness concerns. As long as co-op advertising can bring extra profit to the manufacturer, the retailer’s fairness concerns could improve the effectiveness of the co-op advertising. (5) There exists a Pareto improvement for the profits of both the manufacturer and the retailer when a retailer without fairness concerns becomes fair-minded.     

Periodicity of pricing and marketing efforts in a distribution channel

Most research about cooperative (coop) advertising programs in channels relies on the assumption that manufacturers and retailers decide of pricing and marketing efforts simultaneously. This paper evaluates this central assumption and investigates the optimal periodicity (sequence of move) of pricing and marketing efforts (ME) decisions for a distribution channel. We develop a game theoretic model that accounts for pricing at each level of the channel, for the manufacturer’s ME mix strategies (a direct ME to consumers and coop advertising program offered to the retailer) and the retailer’s ME as well. We obtain solutions for a bilateral channel under different vertical interaction scenarios; when the channel is led by the manufacturer, the retailer or when channel members decide simultaneously of each of their marketing mix decisions (vertical Nash). We compare the effect of pricing and ME decision periodicity on outputs for each channel member. The main findings suggest that simultaneous decision-making of pricing and ME is optimal only for high enough levels of the manufacturer’s ME effects. For very highly effective marketing efforts, sequential play of pricing and ME allows channel members to implement equilibrium strategies and achieve maximum profits that would not be achieved with simultaneous decision-making. This highlights the importance of relaxing the simultaneous play assumption of pricing and ME in a distribution channel.     

Wholesale pricing and evolutionarily stable strategies of retailers with imperfectly observable objective

This paper develops a one-population (indirect) evolutionary game model of a supply chain with one manufacturer/supplier and many (a sufficiently large number of) retailers to study how the retailer’s marketing objective depends on the wholesale price, its observability, the error probability of the observed result on the rival’s preference, the market scale and the retailer’s bargaining power. This paper also presents an algorithm for computing the optimal wholesale price of the manufacturer. We find that the profit (revenue) maximization behavior is an evolutionarily stable marketing strategy if the wholesale price is sufficiently high (low). Given an appropriate wholesale price, the revenue maximization behavior coexists with the profit maximization behavior in the retailers’ population. The larger the market scale, the stronger the motivation of the retailer to take profit maximization behavior due to a higher wholesale price. The cross effects of the retailer’s reservation payoff and the other factors should be considered in the decision process.     

Permanence of delay competitive systems with weak Allee effects

This study discusses a multispecies delay competitive system with weak Allee effects. In the situation where the model is a single species, the weak Allee effect represents a biological mechanism in which an increase in population is beneficial for low densities, but detrimental for high densities. In other words, the per-capita growth rate of each species is formulated by a sign-changing function of population density. In this paper, an existence theorem of positive equilibrium is established using the Brouwer degree theory. For cases without intraspecific delays, it is shown that the system has the property of permanence. Furthermore, a sufficient condition for a positive equilibrium to be globally attractive is obtained by means of the Lyapunov method.