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.     

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,种群密度及种群种内初级种群参数对种群创新输出功能具有较好的支撑功能,且较为稳定,但次级种群参数对创新输出功能的影响整体呈现较弱影响,具有进一步提升空间.据此,提出进一步优化种内关系结构,促进创新输出的相应对策建议.     

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.     

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.     

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.