Abstract
The diffusion of ideas is often closely connected to the creation and diffusion of knowledge and to the technological evolution of society. Because of this, knowledge creation, exchange and its subsequent transformation into innovations for improved welfare and economic growth is briefly described from a historical point of view. Next, three approaches are discussed for modeling the diffusion of ideas in the areas of science and technology, through (i) deterministic, (ii) stochastic, and (iii) statistical approaches. These are illustrated through their corresponding population dynamics and epidemic models relative to the spreading of ideas, knowledge and innovations. The deterministic dynamical models are considered to be appropriate for analyzing the evolution of large and small societal, scientific and technological systems when the influence of fluctuations is insignificant. Stochastic models are appropriate when the system of interest is small but when the fluctuations become significant for its evolution. Finally statistical approaches and models based on the laws and distributions of Lotka, Bradford, Yule, Zipf–Mandelbrot, and others, provide much useful information for the analysis of the evolution of systems in which development is closely connected to the process of idea diffusion.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For example, at Gordon Research Conferences, it is forbidden to take written notes and to quote participant interventions later.
- 2.
For example, take the scientific disciplines and the number of publications as axes.
- 3.
Let us mention a curious and interesting fact connected to statistical indicators. Very interesting is the conclusion in Gao and Guan (2009) that the scale-independent indicators show that in the fast growing innovation system of China, research institutions financed by the government play a more important role than the enterprises.
References
Allen JC (1975) Mathematical model of species interactions in time and space. Am Nat 109(967):319–342 (DOI: 10.1086/283000, stable JSTOR URL: http://www.jstor.org/stable/2459697)
Amabile TM, Conti R, Coon H, Lazenby J, Herron M (1996) Assessing the work environment for creativity. Acad Manage Rev 39(5):1154–1184 (DOI: 10.2307/256995)
Anderson RM, May RM (eds) (1982) Population biology of infectious diseases: Report of the Dahlem workshop on population biology of infectious disease agents, Berlin 1982, March 14–19. Dahlem Workshop Reports. Life Sciences Research Reports, vol 25. Springer, Berlin
Antonelli C (1996) Localized knowledge percolation processes and information networks. J Evol Econ 6(3):281–295 (DOI: 10.1007/BF01193634)
Ausloos M, Lambiotte R, Scharnhorst A, Hellsten I (2008) Andrzej Pȩkalski networks of scientific interests with internal degrees of freedom through self-citation analysis. Int J Mod Phys C 19(3):371–384 (DOI10.1142/S0129183108012224), also available as arXiv preprint http://arxiv.org/abs/0710.1800
Ausloos M (2010) On religion and language evolutions seen through mathematical and agent based models. In: Rangacharyulu C, Haven E (eds) Proceedings of the first interdisciplinary CHESS interactions conference: Saskatoon, Saskatchewan, Canada, 17–20 August 2009. World Scientific, Singapore, pp 157–182 (DOI: 10.1142/9789814295895_0009 DOI:10.1142/9789814295895_0009), also available as arXiv preprint http://arxiv.org/abs/1103.5382arXiv:1103.5382
Barro RJ, Sala-i-Martin X (2004) Economic growth, 2nd edn. MIT Press, Cambridge, MA
Bartholomew DJ (1982) Stochastic models for social processes, 3rd edn. Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics. Wiley, Chichester
Becker GS, Murphy KM (1988) A theory of rational addiction. J Polit Econ 96(4):675–700 (DOI: 10.1086/261558, stable JSTOR URL: http://www.jstor.org/stable/1830469)
Becker GS (1996) Accounting for tastes. Harvard University Press, Cambridge, MA
Bernius S (2010) The impact of open access on the management of scientific knowledge. Online Inf Rev 34(4):583–603 (DOI: 10.1108/14684521011072990)
Bettencourt LMA, Cintrón-Arias A, Kaiser DI, Castillo-Chávez C (2006) The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models. Physica A 364:513–536 (DOI: 10.1016/j.physa.2005.08.083), also available as arXiv preprint http://arxiv.org/abs/physics/050206
Bettencourt LMA, Kaiser DI, Kaur J, Castillo-Chávez C, Wojick DE (2008) Population modeling of the emergence and development of scientific fields. Scientometrics 75(3):495–518 (DOI: 10.1007/s11192-007-1888-4)
Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: Structure and dynamics. Phys Rep 424(4–5):176–308 (DOI: 10.1016/j.physrep.2005.10.00)
Bourdieu P (1986) Forms of capital. In: Richardson JG (ed) Handbook of theory and research for the sociology of education. Greenwood, New York, NY, pp 241–258
Braun T, Glänzel W, Schubert A (1985) Scientometric indicators: A 32-country comparative evaluation of publishing performance and citation impact. World Scientific, Singapore
Brauer F, Castillo-Chavez C (2001) Mathematical models in population biology and epidemiology. Texts in Applied Mathematics, vol 40. Springer, New York, NY
Bruckner E, Ebeling W, Scharnhorst A (1989) Stochastic dynamics of instabilities in evolutionary systems. Syst Dyn Rev 5(2):176–191 (DOI: 10.1002/sdr.4260050206)
Bruckner E, Ebeling W, Scharnhorst A (1990) The application of evolution models in scientometrics. Scientometrics 18(1):21–41 (DOI: 10.1007/BF02019160)
Bruckner E, Ebeling W, Jiménez-Montaño MA, Scharnhorst A (1996) Nonlinear stochastic effects of substitution – an evolutionary approach. J Evol Econ 6(1):1–30 (DOI: 10.1007/BF01202370)
Bryman A (1988) Quantity and quality in social research. Contemporary Social Research Series, vol 18. Unwin Hyman, London
Burrell QL (2007) Hirsch’s h-index: A stochastic model. J Informetr 1(1):16–25 (DOI: 10.1016/j.joi.2006.07.001)
Casetti E, Semple RK (1969) Concerning the testing of spatial diffusion hypotheses. Geogr Anal 1(3):254–259 (DOI: 10.1111/j.1538-4632.1969.tb00622.x)
Castiaux A (2007) Radical innovation in established organizations: Being a knowledge predator. J Eng Tech Manag 24(1–2):36–52 (DOI: 10.1016/j.jengtecman.2007.01.003)
Chen C, Hicks D (2004) Tracing knowledge diffusion. Scientometrics 59(2):199–211 (DOI: 10.1023/B:SCIE.0000018528.59913.48)
Chen YS, Cheng PP, Tong Y (1993) Theoretical foundation of the 80/20 rule. Scientometrics 28(2):183–204 (DOI: 10.1007/BF02016899)
Chung KH, Cox RAK (1990) Patterns of productivity in the finance literature: A study of the bibliometric distributions. J Finance 45(1):301–309 (DOI: 10.2307/2328824DOI:10.2307/2328824, stable JSTOR URL: http://www.jstor.org/stable/2328824)
Coleman JC (1988) Social capital in the creation of human capital. Am J Sociol 94(Suppl):S95–S120. (DOI: 10.1086/228943, stable JSTOR URL: http://www.jstor.org/stable/2780243)
Cowan R, Foray D (1997) The economics of codification and the diffusion of knowledge. Ind Corp Change 6(3):595–622 (DOI: 10.1093/icc/6.3.595)
Dahlman C, Zhihua Zeng D, Wang S (2007) Enhancing China’s competitiveness through life long learning. The World Bank, Washington, DC
Dahlman C (2009) Different innovation strategies, different results: Brazil, Russia, India, China and Korea (the BRICKs). In: Chandra V, Eröcal D, Padoan PC, Primo Braga AC (eds) Innovation and growth: Chasing a moving frontier. OECD, Paris; International Bank for Reconstruction and Development/The World Bank, Washington, DC, pp 131–168, available online at the URL: http://www.oecd.org/document/35/0,3343,en_2649_37417_44268835_1_1_1_37417,00.html
Daley DJ (1967) Concerning the spread of news in a population of individuals who never forget. Bull Math Biol 29(2):373–376 (DOI: 10.1007/BF02476908)
Davis JB (2003) The theory of the individual in economics: Identity and value. Routledge Advances in Social Economics. Routledge, London (DOI: 10.4324/9780203457689)
Dietz K (1967) Epidemics and rumours: A survey. J R Stat Soc Ser A 130(4):505–528 (DOI: 10.2307/2982521, stable JSTOR URL: http://www.jstor.org/stable/2982521)
Dimitrova ZI, Vitanov NK (2000) Influence of adaptation on the nonlinear dynamics of a system of competing populations. Physc Lett A 272(5–6):368–380 (DOI: 10.1016/S0375-9601(00)00455-2)
Dimitrova ZI, Vitanov NK (2001) Adaptation and its impact on the dynamics of a system of three competing populations. Physica A 300(1–2):91–115 (DOI: 10.1016/S0378-4371(01)00330-2)
Dimitrova ZI, Vitanov NK (2001) Dynamical consequences of adaptation of the growth rates in a system of three competing populations. J Phys A Math Gen 34(37):7459–7473 (DOI: 10.1088/0305-4470/34/37/303)
Dimitrova ZI, Vitanov NK (2004) Chaotic pairwise competition. Theor Popul Biol 66(1):1–12 (DOI: 10.1016/j.tpb.2003.10.008)
Dodd SC (1958) Formulas for spreading opinions. Public Opin Q 22(4):537–554 (DOI: 10.1086/266827, stable JSTOR URL: http://www.jstor.org/stable/2746601)
Dolfsma W (2008) Knowledge economies: Organization, location and innovation. Routledge Studies in Global Competition, vol 39. Routledge, London
Ebeling W, Engel A, Mazenko VG (1986) Modeling of selection processes with age-dependent birth and death rates. BioSystems 19(3):213–221 (DOI: 10.1016/0303-2647(86)90040-7)
Ebeling W, Engel A, Feistel R (1990) Physik der Evolutionsprozesse. Akademie-Verlag, Berlin
Ebeling W, Feistel R, Hartmann-Sonntag I, Schimansky-Geier L, Scharnhorst A (2006). New species in evolving networks – stochastic theory of sensitive networks and applications on the metaphorical level. BioSystems 85(1):65–71 (DOI: 10.1016/j.biosystems.2006.02.013)
Ebeling W, Scharnhorst A (1985) Selforganization models for field mobility of physicists. Czech J Phys 36(1):43–46 (DOI: 10.1007/BF01599723)
Ebeling W, Scharnhorst A (2000) Evolutionary models of innovation dynamics. In: Helbing D, Herrmann HJ, Schreckenberg M, Wolf DE (eds) Traffic and granular flow’ 99. Social, traffic and granular dynamics. Springer, Berlin, pp 43–56
Edelstein-Keshet L (1988) Mathematical models in biology. The Random House/Birkhäuser Mathematics Series. Random House, New York, NY
Egghe L (1998) Mathematical theories of citation. Scientometrics 43(1):57–62 (DOI: 10.1007/BF02458394)
Egghe L, Rousseau R (1990) Introduction to informetrics: Quantitative methods in library, documentation and information science. Elsevier, Amsterdam
Epstein JM (1997) Nonlinear dynamics, mathematical biology, and social science. Santa Fe Institute Studies in the Sciences of Complexity. Lecture Note, vol 4. Addison-Wesley, Reading, MA
Fernández-Camo A, Toralbo M, Vallejo M (2004) Reconsidering Price’s model of scientific growth: An overview. Scientometrics 61(3):301–321 (DOI: 10.1023/B:SCIE.0000045112.11562.11)
Foray D (2004) The economics of knowledge. MIT Press, Cambridge, MA. Revised and extended translation of: Foray D (2000) L’conomie de la connaissance. La Decouverte, Paris
Gao X, Guan J (2009) A scale-independent analysis of the performance of the Chinese innovation system. J Informetr 3(4):321–331 (DOI: 10.1016/j.joi.2009.04.004)
Gardiner CW (1983) Handbook of stochastic methods for physics, chemistry and the natural sciences. Springer Series in Synergetics, vol 13. Springer, Berlin
Gause GF (1934) The struggle for existence. Williams and Wilkins, Baltimore, MD
Geroski PA (2000) Models of technology diffusion. Res Policy 29(4):603–625 (DOI: 10.1016/S0048-7333(99)00092-X)
Gilbert GN (1978) Measuring the growth of science: A review of indicators of scientific growth. Scientometrics 1(1):9–34 (DOI: 10.1007/BF02016837)
Glänzel W, Schoepflin U (1994) A stochastic model for the ageing of scientific literature. Scientometrics 30(1):49–64 (DOI: 10.1007/BF02017212)
Goffman W (1966) Mathematical approach to the spread of scientific ideas – the history of mast cell research. Nature 212(5061):449–452 (DOI: 10.1038/212449a0)
Goffman W, Newill VA (1964) Generalization of epidemic theory: An application to the transmission of ideas. Nature 204(4955):225–228 (DOI: 10.1038/204225a0)
Haitun SD (1982) Stationary scientometric distributions. Part II. Non-Gaussian nature of scientific activities. Scientometrics 4(2):89–104 (DOI: 10.1007/BF02018448)
Hänggi P, Thomas H (1982) Stochastic processes: Time evolution, symmetries and linear response. Phys Rep 88(4):207–319 (DOI: 10.1016/0370-1573(82)90045-X)
Hellsten I, Lambiotte R, Scharnhorst A, Ausloos M (2006) A journey through the landscape of physics and beyond – the self-citation patterns of Werner Ebeling. In: Pöschel T, Malchow H, Schimansky–Geier L (eds) Irreversible Prozesse und Selbstorganisation. Logos Verlag, Berlin, pp 375–384
Hellsten I, Lambiotte R, Scharnhorst A, Ausloos M (2007) Self-citations, co-authorships and keywords: A new method for detecting scientists field mobility? Scientometrics 72(3):469–486 (DOI: 10.1007/s11192-007-1680-5)
Hellsten I, Lambiotte R, Scharnhorst A, Ausloos M (2007) Self-citation networks as traces of scientific careers. In: Torres-Salinas D, Moed H (eds) Proceedings of the ISSI 2007, 11th International Conference of the International Society for Scientometrics and Informetrics, CSIC, Madrid, Spain, June 25–27, 2007. CINDOC-CSIC, Madrid, vol 1, pp 361–367
Hirsch JE (2005) An index to quantify an individual’s scientific research output. Proc Natl Acad Sci USA 102(46):16569–16572 (DOI: 10.1073/pnas.0507655102, stable JSTOR URL: http://www.jstor.org/stable/4152261), also available as arXiv preprint http://arxiv.org/abs/physics/0508025
Howells JRL (2002) Tacit knowledge, innovation and economic geography. Urban Stud 39(5–6):871–884 (DOI: 10.1080/00420980220128354)
Ivanova K, Ausloos M (1999) Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking. Physica A 274(1–2):349–354 (DOI: 10.1016/S0378-4371(99)00312-X)
Jaffe AB (1986) Technological opportunity and spillovers of R&D: Evidence from firms patents, profits, and market value. Am Econ Rev 76(5):984–1001 (stable JSTOR URL: http://www.jstor.org/stable/1816464), also availabe online as National Bureau of Economic Research (NBER) Working Paper No. 1815 at the URL: http://www.nber.org/papers/w1815
Jaffe AB, Trajtenberg M (eds) (2002) Patents, citations and innovations: A window on the knowledge economy. MIT Press, Cambridge, MA
Karmeshu (1982) Time lag in a diffusion model of information. Math model 3(2):137–141 (DOI: 10.1016/0270-0255(82)90018-5)
Katz JS (1999) The self-similar science system. Res Policy 28(5):501–517 (DOI: 10.1016/S0048-7333(99)00010-4)
Kealey T (2000) More is less. Economists and governments lag decades behind Derek Price’s thinking. Nature 405(6784):279–279 (DOI: 10.1038/35012717)
Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc Lond A Math Phys Character 115(772):700–721 (DOI: 10.1098/rspa.1927.0118, stable JSTOR URL: http://www.jstor.org/stable/94815)
Kerner EH (1959) Further considerations on the statistical mechanics of biological associations. Bull Math Biol 21(2):217–253 (DOI: 10.1007/BF02476361)
Keynes JM (1930) A treatise on money. 2 Volumes. Harcourt, Brace and Co., New York, NY. Reprinted in: Keynes JM (1971, 1989, 2nd edn) The collected writings of John Maynard Keynes: Volume V: A treatise on money: In two volumes: 1. The pure theory of money, Volume VI: A treatise on money: In two volumes: 2. The applied theory of money. Macmillan, London
Kiss IZ, Broom M, Graze PG, Rafols I (2000) Can epidemic models describe the diffusion of topics across disciplines. J Infometr 4(1):74–82 (DOI: 10.1016/j.joi.2009.08.002), also available as arXiv preprint http://arxiv.org/abs/0905.3585
Kiss IZ, Green DM, Kao RR (2005) Disease contact tracing in random and clustered networks. Proc R Soc B Biol Sci 272(1570):1407–1414 (DOI: 10.1098/rspb.2005.3092, stable JSTOR URL: http://www.jstor.org/stable/30047699)
Kot SM (1987) The stochastic model of evolution of scientific disciplines. Scientometrics 12(3–4):197–205 (DOI: 10.1007/BF02016292)
Kucharavy D, Schenk E, de Guio R (2009) Long-run forecasting of emerging technologies with logistic models and growth of knowledge. In: Roy R, Shehab E (eds) Proceedings of the 19th CIRP design conference – competitive design, Cranfield, UK. Cranfield University, Cranfield, pp 277–284, available online at the URL: http://dspace.lib.cranfield.ac.uk/handle/1826/3730
Kuhn TS (1962) The structure of scientific revolutions. University of Chicago Press, Chicago, IL
Lal VB, Karmeshu, Kaicker S (1988) Modeling innovation diffusion with distributed time lag. Technol Forecast Soc Change 34(2):103–113 (DOI: 10.1016/0040-1625(88)90060-1)
Leydesdorff L (2006) The knowledge-based economy: Modeled, measured, simulated. Universal Publishers, Boca Raton, FL
Li W (2002) Zipf’s law everywhere. Glottometrics 5:15–41, available online at the URL: http://www.nslij-genetics.org/wli/pub/glottometrics02.pdf
Lotka AJ (1912) Ein Fall von Autokatakinese mit oscillatorischem Verlauf. Zeitschrift für Physikalische Chemie, Stöchiometrie und Verwandtschaftslehre 80(2):159–164
Lotka AJ (1925) Elements of physical biology. Williams & Wilkins Company, Baltimore, MD, available online at the URL: http://www.archive.org/details/elementsofphysic017171mbp. Reprinted as: Lotka AJ (1956) Elements of mathematical biology. Dover Books on the Biological Sciences. Dover Publications, New York, NY
Lotka AJ (1926) The frequency distribution of scientific productivity. J Wash Acad Sci 16(12):317–323
Ma Z, Li J (eds) (2009) Dynamical modeling and analysis of epidemics. World Scientific, Singapore, available online at the URL: http://ebooks.worldscinet.com/ISBN/9789812797506/9789812797506.html
Magyari-Beck I (1984) A method of measurement of scientific production quality. Science of Science 4(2):183–195
Mahajan V, Peterson RA (1985) Models for innovation diffusion. Quantitative Applications in the Social Sciences, vol 48. Sage Publications, Beverly Hills, CA
Mansfield E (1961) Technical change and the rate of imitation. Econometrica 29(4):741–766 (DOI: 10.2307/1911817, stable JSTOR URL: http://www.jstor.org/stable/191181)
Marshall A (1920) Principles of economics: An introductory volume, 8th edn. McMillan, London, available online ((1907) 5th edn) at the URL: http://www.archive.org/details/principlesofecon01marsuoft
May RM (1974) Stability and complexity in model ecosystems, 2nd edn. Monographs in Population Biology, vol 6. Princeton University Press, Princeton, NJ
Meade N, Islam T (1995) Forecasting with growth curves: An empirical comparison. Int J Forecast 11(2):199–215 (DOI: 10.1016/0169-2070(94)00556-R)
Meyer PS (1994) Bi-logistic growth. Technol Forecast Soc Change 47(1):89–102 (DOI: 10.1016/0040-1625(94)90042-6)
Meyer PS, Yung JW, Ausubel JH (1999) A primer on logistic growth and substitution: The mathematics of the Loglet Lab software. Technol Forecast Soc Change 61(3):247–271 (DOI: 10.1016/S0040-1625(99)00021-9)
Modis T (2003) A scientific approach to managing competition. Ind Physicist 9(1):24–27, available online at the URL: http://www.aip.org/tip/INPHFA/vol-9/iss-1/p25.html
Modis T (2007) Strengths and weaknesses of S-curves. Technol Forecast Soc Change 74(6):866–872 (DOI: 10.1016/j.techfore.2007.04.005)
Morone P, Taylor R (2010) Knowledge diffusion and innovation: Modelling complex entrepreneurial behaviours. Edward Elgar Publishing Inc., Northampton, MA
Murray JD (1989) Mathematical biology. Biomathematics, vol 19. Springer, Berlin
Nonaka I (1994) A dynamic theory of organizational knowledge creation. Organ Sci 5(1):14–37 (DOI: 10.1287/orsc.5.1.14, stable JSTOR URL: http://www.jstor.org/stable/2635068)
Nonaka I, Takeuchi H (1995) The knowledge creating company: How Japanese companies create the dynamics of innovation. Oxford University Press, Oxford
Nonaka I, Konno N (1998) The concept of “Ba”: Building a foundation for knowledge creation. Calif Manage Rev 40(3):40–54 (DOI: 10.1225/CMR107)
Nowakowska M (1973) Epidemical spread of scientific objects: An attempt of empirical approach to some problems of meta-science. Theory Decis 3(3):262–297 (DOI: 10.1007/BF00139506)
Noyons ECM, Van Raan AFJ (1998) Advanced mapping of science and technology. Scientometrics 41(1–2):61–67 (DOI: 10.1007/BF02457967)
Odum EP (1959) Fundamentals of ecology. W.B. Saunders, Philadelphia, PA
Okubo A (1980) Diffusion and ecological problems: Mathematical models. Biomathematics, vol 10. Springer, Berlin. Extended translation of: Okubo A (1975) Seitaigaku to kakusan. Tukijishokan, Tokyo
Plesk PE (1997) Creativity, innovation and quality. ASQ Quality Press, Milwaukee, WI
Price DJ de Solla (1951) Quantitative measures of the development of science. Archives Internationale d’Histoire de Sciences 4(14):86–93, available online at the URL: http://garfield.library.upenn.edu/price/pricequantitativemeasures1951.pdf
Price DJ de Solla (1956) The exponential curve of science. Discovery 17(1):240–243. Reprinted in: Barber B, Hirsch W (eds) (1962) The sociology of science. The Free Press of Glencoe, New York, NY, pp 516–524
Price DJ de Solla (1961) Science since Babylon. Yale University Press, New Haven, CT
Price DJ de Solla (1963) Little science, big science. Columbia University Press, New York, NY
Price DJ de Solla (1971) Principles for projecting funding of academic science in the 1970s. Sci Stud 1(1):85–94 (DOI: 10.1177/030631277100100106, stable JSTOR URL: http://www.jstor.org/stable/370198)
Price DJ de Solla (1976) A general theory of bibliometric and other cumulative advantage processes. J Am Soc Inf Sci 27(5):292–306 (DOI: 10.1002/asi.4630270505), also available online at the URL: http://www.asis.org/Publications/JASIS/Best\_Jasist/1976pricejasistarticle.pdf
Price DJ de Solla, Gürsey S (1975) Some statistical results for the numbers of authors in the states of the United States and the nations of the world. In: Who is publishing in science 1975 annual. Institute for Scientific Information, Philadelphia, PA, pp 26–34
Putnam RD, Leonardi R, Nanetti RY (1993) Making democracy work: Civic transitions in modern Italy. Princeton University Press, Princeton, NJ
Risken H (1984) The Fokker-Planck equation: Methods of solution and applications. Springer Series in Synergetics, vol 18. Springer-Verlag, Berlin
Rogers E (1962) Diffusion of innovations. The Free Press, New York, NY; Collier-MacMillan, London
Romanov AK, Terekhov AI (1997) The mathematical model of productivity- and age-structured scientific community evolution. Scientometrics 39(1):3–17 (DOI: 10.1007/BF02457427)
Romer PM (2002) When should we use intellectual property rights? Am Econ Rev 92(2):213–216 (DOI: 10.1257/000282802320189276, stable JSTOR URL: http://www.jstor.org/stable/3083404). The article is part of: Baldwin JE, Oaxaca RL (eds) Papers and proceedings of the one hundred fourteenth annual meeting of the American Economic Association, Atlanta, GA, January 4–6, 2002. Am Econ Rev 92(2):1–478
Romer PM (1994a) The origins of endogeneous growth. J Econ Perspect 8(1):3–22 (stable JSTOR URL: http://www.jstor.org/stable/2138148)
Romer PM (1994b) New goods, old theory, and the welfare costs of trade restrictions. J Dev Econ 43(1):5–38 (DOI: 10.1016/0304-3878(94)90021-3), also availabe online as National Bureau of Economic Research (NBER) Working Paper No. 4452 at the URL: http://www.nber.org/papers/w4452
Romer D (1996) Advanced macroeconomics. McGraw-Hill, New York, NY
Saviotti PP (1999) Knowledge, information and organisational structures. In: Robertson PL (ed) Authority and control in modern industry: Theoretical and empirical perspectives. Routledge Studies in Business Organization and Networks, vol 10. Routledge, London, pp 120–139 (DOI: 10.4324/9780203435403.ch4)
Scharnhorst A (1998) Citation networks, science landscapes and evolutionary strategies. Scientometrics 43(1):95–106 (DOI: 10.1007/BF02458399)
Scharnhorst A (2001) Constructing knowledge landscapes within the framework of geometrically oriented evolutionary theories. In: Matthies M, Malchow H, Kriz J (eds) Integrative systems approaches to natural and social dynamics. Springer, Berlin, pp 505–515
Sharif MN, Ramanathan K (1981) Binomial innovation diffusion models with dynamic potential adopter population. Technol Forecast Soc Change 20(1):63–87 (DOI: 10.1016/0040-1625(81)90041-X)
Small H (1997) Update on science mapping: Creating large document spaces. Scientometrics 38(2):275–293 (DOI: 10.1007/BF02457414)
Small H (1998) A general framework for creating large-scale maps of science in two or three dimensions: The SciViz system. Scientometrics 41(1–2):125–133 (DOI: 10.1007/BF02457973)
Small H (2006) Tracking and predicting growth areas in science. Scientometrics 68(3):595–610 (DOI: 10.1007/s11192-006-0132-y)
Soler JM (2007) A rational indicator of scientific creativity. J Informetr 1(2):123–130 (DOI: 10.1016/j.joi.2006.10.004), also available as arXiv preprint http://arxiv.org/abs/physics/0608006
Solomon S, Richmond P (2001) Power laws of wealth, market order volumes and market returns. Physica A 299(1–2):188–197 (DOI: 10.1016/S0378-4371(01)00295-3), also available as arXiv preprint http://arxiv.org/abs/cond-mat/0102423
Solomon S, Richmond P (2002) Stable power laws in variable economics; Lotka–Volterra implies Pareto–Zipf. Eur Phys J B 27(2):257–261 (DOI: 10.1140/epjb/e20020152)
Stiglitz JE (1987) Learning to learn, localized learning and technological progress. In: Dasgupta P, Stoneman P (eds) Economic policy and technological performance. Cambridge University Press, Cambridge, pp 125–153
Szydlowski M, Krawiez A (2001) Scientific cycle model with delay. Scientometrics 52(1):83–95 (DOI: 10.1023/A:1012751028630)
Szydlowski M, Krawiez A (2009) Growth cycles of knowledge. Scientometrics 78(1):99–111 (DOI: 10.1007/s11192-007-1958-7)
Vandewalle N, Ausloos M (1997) Coherent and random sequences in financial fluctuations. Physica A 246(3–4):454–459 (DOI: 10.1016/S0378-4371(97)00366-X)
van Kampen NG (1981) Stochastic processes in physics and chemistry. North-Holland Publishing Company, Amsterdam
van Raan AFJ (1997) Scientometrics: State of art. Scientometrics 38(1):205–218 (DOI: 10.1007/BF02461131)
van Raan AFJ (2000) On growth, ageing and fractal differentiation of science. Scientometrics 47(2):347–362 (DOI: 10.1023/A:1005647328460)
Vitanov NK, Dimitrova ZI, Kantz H (2006) On the trap of extinction and its elimination. Phys Lett A 349(5):350–355 (DOI: 10.1016/j.physleta.2005.09.043)
Vitanov NK, Dimitrova ZI, Ausloos M (2010) Verhulst-Lotka–Volterra (VLV) model of ideological struggle. Physica A 389(21):4970–4980 (DOI: 10.1016/j.physa.2010.06.032), also available as arXiv preprint http://arxiv.org/abs/1103.5362
Vitanov NK, Jordanov IP, Dimitrova ZI (2009) On nonlinear population waves. Appl Math Comput 215(8):2950–2964 (DOI: 10.1016/j.amc.2009.09.041)
Vitanov NK, Jordanov IP, Dimitrova ZI (2009) On nonlinear dynamics of interacting populations: Coupled kink waves in a system of two populations. Commun Nonlinear Sci Numer Simul 14(5):2379–2388 (DOI: 10.1016/j.cnsns.2008.07.015)
Volterra V (1927) Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Memorie della Classe di Scienze Fisiche, Matematiche e Naturali, Accademia Nazionale dei Lincei, Roma, 6th series, 2(3):31–113. English translation: Variations and fluctuations of the number of individuals in animal species living together. In: Chapman RN (1931) Animal ecology. McGraw Hill, New York, NY, pp 409–448
Wagner-Döbler R, Berg J (1994) Regularity and irregularity in the development of scientific disciplines: The case of mathematical logics. Scientometrics 30(1):303–319 (DOI: 10.1007/BF02017230)
Walsh JR (1935) Capital concept applied to man. Q J Econ 49(2):255–285 (DOI: 10.2307/1884067, stable JSTOR URL: http://www.jstor.org/stable/1884067)
Willson WG, de Roos AM (1993) Spatial instabilities within the diffusive Lotka–Volterra system: Individual-based simulation results. Theor Popul Biol 43(1):91–127 (DOI: 10.1006/tpbi.1993.1005)
Wright S (1932) The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Jones DF (ed) Proceedings of the Sixth International Congress of Genetics. Brooklyn Botanic Garden, Brooklyn, NY, part 1, pp 356–366, available online at the URL: http://www.esp.org/books/6th-congress/facsimile/contents/6th-cong-p356-wright.pdf
Yablonsky AI (1980) On fundamental regularities of the distribution of scientific productivity. Scientometrics 2(1):3–34 (DOI: 10.1007/BF02016597)
Yablonsky AI (1985) Stable non-Gaussian distributions in scientometrics. Scientometrics 7(3–6):459–470 (DOI: 10.1007/BF02017161)
Ziman JM (1969) Information, communication, knowledge. Nature 224(5217):318–324 (DOI: 10.1038/224318a01)
Zipf GK (1949) Human behavior and the principle of least effort: An introduction to human ecology. Addison-Wesley, Cambridge, MA
Acknowledgements
Thanks to the editors of the book for inspiring us into writing this work. The authors gratefully acknowledge stimulating discussions with many wonderful colleagues at several meetings of the ESF Action COST MP-0801 ‘Physics of Competition and Conflict’.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Vitanov, N.K., Ausloos, M.R. (2012). Knowledge Epidemics and Population Dynamics Models for Describing Idea Diffusion. In: Scharnhorst, A., Börner, K., van den Besselaar, P. (eds) Models of Science Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23068-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-23068-4_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23067-7
Online ISBN: 978-3-642-23068-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)