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• 1. T.R. Malthus An essay on the principle of population
• printed for J Johnsonin St Paul's Churchyard, London 1798
• reprinted by Macmillan et Co 1894)
• 2. P.F. Verhuulst Notice sur la Loi que la Population Suit
• dans son Accroissement;
• Correspondence Mathematique et Physique
• publie par A Quetelet 10 (1838) pp 113-121;
• (English translation in D. Smith and N. Keyfiz
• Mathematical Demography
• Springer NY 1977 pp 333-337)
• Mem. Acad Roy Bruxelles 28(1844) 1)
• 3. J Davison Trans. Roy. Soc. South Aus. 62 (1938) 342
• 4. E.W. Montroll and W.W. Badger
• Introduction to Quantitative aspects of Social Phenomena
• North Holland Amsterdam 1984
• 5. E.W. Montroll PNAS USA 75 (1978) 4633
• 6. J. Salk The Survival of the Wisest Columbia U Press NY 1983
• 7. N. Goel, S. Maitra and E.W. Montroll Rev Mod Phys 43 (1971) 231
• 7.b Population Dynamics in a homogenous Environment
• TM Hallam p 61-94 i
• in Biomathematics Vol 17 Mathematical Ecology
• Ed TG Hallam and SA Levin
• Springer Verlag Berlin Heidelberg 1986
• 7. Coleman, J.S., Katz, E., and Menzel, H. (1966). Medical Innovation: A Diffusion Study.
• Bobbs­Merrill, New York.
• Ryan B. and Gross, N.C. (1943). ''The Diffusion of Hybrid Seed Corn in Two Iowa
• Communities,'' Rural Sociology, 8, 15.
• Rogers, E. M. (1995). The Diffusion of Innovations, 4th, New York: Free Press.
• Sultan, F., Farley, J. U., and Lehmann, D. R. (1990). ''A Meta Analysis of Applications
• of Diffusion Models,'' Journal of Marketing Research, 27, 70.
• Mahajan, V., Muller, E., and Bass, F. M. (1990). ''New Product Diffusion Models in
• Marketing: A Review and Directions for Research,''Journal of Marketing, 54, 1.
• Rogers E. and Kincaid, D.L. (1981). Communication Networks: A New Paradigm for
• Research. New York: Free Press.
• Bass, F. M., (1969). ''A New Product Growth Model for Consumer Durables,'' Man­
• agement Science, 15, 215.
• Parker, P. M. (1994).''Aggregate Diffusion Models in Marketing: A Critical Review,''
• International Journal of Forecasting 10, 353.
• 8 J.C. Fisher and R.C. Pry in
• Practical Applications of Technological Forecasting in Industry
• ed M.J. Cetron, Chichester, NY 1971.
• 9. E.W. Montroll and B.J. West in Synergetics ed H. Haken 1986 Teubner Stuttgart 1973
• 10. D. Sahal Patters of Technological Innovation
• Addison Wesley London 1981
• 11. Solomon et al Social Percolation , Goldenberg et al. Marketing Percolation
• 12. J.S. Coleman Introduction to Mathematical Sociology
• The Free Press of Glencoe, Collier-Macmillan, London 1964
• 13. G.J Paulik
• "Digital Simulation of natural animal communities"
• in
• "Pollution and marine Ecology" TA Olson and FG Burgess Eds
• Wiley - Interscience 1967
• 14. R. Ross "The prevention of malaria" ; John Murray London 1911
• 15. Alfred J. Lotka
• Quantitative Studies in Epidemiology Nature Feb 1912 p 497,
• Science Progress 1920 v 14, p413
• A.J. Lotka Reation between birth rates and death rates
• Science 26 (1907) 21-22
• A.J. Lotka Die Evolution vom Standpunkte der Physik
• Ostwalds Annalen der Naturphilosophie 10 (1911) 59
• A.J. Lotka Elements of Physical Bilology Williams and Wilkins
• Baltimore MD 1924 (and Dover NY 1956)
• 16. A.J. Lotka Contribution to the analysis of malaria
• epidemiology Supplement to the Amer J Hygiene
• parts I p 1-37 , II pp 38-54 and III pp 55-95.
• 17 Vito Volterra Sui tentativi di applicazione della matematiche alle
• scienze biologicha e sociale
• Giornale degli Economisti 23 (1901) 436-458
• V. Volterra Les mathematiques dans les sciences biologiques et
• sociales La Revue du mois , Paris 1 (1906) 1-20).
• 18. Francesco M Scudo and James R Ziegler The golden age of
• Theoretical Ecology: 1923-1940 Lecture Notes in
• Biomathematics Managing Editor S Levin
• Sprienger-Verlag New York 1978 ).
• 18 V.A. Kostitzin The logistic law and its generalizations
• Acta biotheoretica 5 (1940) 155-159)
• 19. V.A. Kostitzin Sur la segregation physiologique et la
• variation des especes. Acta Biotheoretica 5 (1940) 160.
• 20. V.A. Kostitzin Symbiose, parasitisme and evolution
• Hermann 1934 Paris.
• 21. Vito Volterra "Variations and Fluctuations of the
• Number of individuals in animal
• Species living together"
• In Chapman R N "Animal ecology with especial reference to
• insects Mc Graw Hill NY 1931
• translated from the french version in
• Journal du Conseil international pour l'exploitation de la mer II,
• Vol 1 , 1928 (a translation from the original text (Volterra 1926).
• Variazioni e flutuazioni del numero d'individui
• in specie animali conviventi.
• Mem Accad Lincei (6) 1926 31-113
• see also the adnotated translation in
• Francesco M Scudo and James R Ziegler The golden age of
• Theoretical Ecology: 1923-1940 Lecture Notes in
• Biomathematics Managing Editor S Levin
• Sprienger-Verlag New York 1978 ).
• 22. A. Kolmogoroff Sulla teoria di Volterra dell lotta per lesistenza
• Giorn Instituto Ital. Attuari 7 (1936) 74-80)
• 23. Manfred Peshel and Werner Mende The Predator-Prey Model;
• Do we live in a Volterra World? Springer Verlag, Wien , NY 1986
• 24. J Hofbauer and K Sigmund
• The theory of evolution and Dynamical Systems
• London Mathematical Society Student Texts 7
• Cambridge Univ Press 1988
• 24. J Maynard Smith Models in Ecology Cambridge U press 1974 p 104
• and
• May RM Will a large complex system be stable? Nature 238 (1972) 413-14
• 36. M Eigen Naturweissenschaften 58 (1971) 465
• 37. M Eigen and P Schuster The Hypercycle
• Springer Berlin Heidelberg 1979
• 38. P Schuster Physica 22 D (1986) 100-119
• L.D. Landau E.M. Lifshitz course of theoretical physics vol 3
• quantum mechanics (pergamon oxford 1977) S38
• J. Schumpeter the theory of economic development
• Harvard Univ. Press Cambridge 1934
• A.A. Alcian J. Political Economy 58 (1951) 211 222
• R.R. Nnelson S.G. Winter
• An Evolutionary Theory of Economic Change
• Harvard Univ Press Cambridge 1982
• M.A. Jimenez Montano and W. Ebeling Collective Phenomena 3 (1980) 107-114
• G. Silverberg
• Modeling Economic Dynamics and Technical Change;
• Mathematical Approaches to Self-Organization and Evolution
• in
• Technical Change and Economic Theory
• ed Dosi et al
• Pinter NY 1988 pp 531-559
• W. Ebeling R. Feistel
• Physik der Selbstorganisation und Evolution
• Akademie-Verlag, Berlin 1982
• N.K. Jerne
• Structural Analogies Between the Immune System and the
• Nervous System in Stability and Origin of Biological Information
• Ed. by I.R. Miller, Wiley NY 1975 pp 201-204
• 25. R.A. Fisher The wave of advance of advantageous genes
• Ann. Eugen. London 7 (1937) 355-369;
• 26. A. Kolmogorov, I Petrovsky and N Piscunov
• Etude de l'equations de la diffusion avec croissance de la quantite
• de la matiere et son application a un probleme biologique
• Bull. Univ. Moscou , Ser. Internation., Sec. A, 1 No 6 (1937) 1-25
• foloowed up by a large literature in physics journals.
• 27. A. Turing The chemical basis of morphogenesis
• Philos. Trans. R. Soc. London Ser. B 237 (1952) 37-72
• 28. S A Levin 1986 Random walk models of movement
• and their implications pp 143-154 in T Hallam and SA Levin
• (eds) Mathematical Ecology : An introduction
• Springer Verlag 1986 Heidelberg.
• 29. S.A. Levin
• Population Models and Community Structure in
• Heterogenous Environments
• pp 439-476
• in
• MAA Studies in Mathematics Vol 16
• Studies in Mathematical Biology
• Part II
• Populations and Communities
• S.A. Levin Editor
• Mathematical Association of America 1978
• 30. H. Kierstead and L.B. Slobodkin
• The Size of Water Masses Containing
• Plancton Blooms J. Mar. Res. 12 (1953) 141-147.
• 31. H. Meinhardt Models of biological formation
• Acad. Press London 1982
• 32. H.T. Banks and K.A. Murpy
• Quantitative Modeling of Growth and Dispersal in Population Models
• Mathematical Topics in population Biology
• E. Teramoto and M. Yamaguti
• Lecture Notes in Biomathematics 71
• Springer Verlag Berlin-Heidelberg 1987
• 33. Masayasu Mimura "Coexistence in Competition-Diffusion Systems"
• in
• Differential Equations, Models in Biology,
• Epidemiology and Ecology
• Proceedings Claremont 1990
• S Busenberg and M Martelly (Eds)
• Springer Verlag Lecture Notes
• in Biomathematics 92 Managing Editor S A Levin
• Berlin 1991
• 34. Norman T. J. Bailey
• Spatial Models in the Epidemiology of infectious diseases
• p 233-260 in
• Biological Growth and Spread
• W. Jager, H. Rost and P. Tautu
• Springer Verlag
• Lecture Notes in Biomathematics 38
• Heidelberg 1980
• 35. S. Rushton and A.J. Mautner (1955) the deterministic model
• of a simple epidemic for more than one community
• Biometrika 42 (1955) 126-132)
• 36. R.M. May and R.M. Anderson
• Thr Transmission of Human Immunodeficiency Virus (HIV)
• Reprinted from Philosophical Transactions ao The Royal Society
• (Discussion Meeting on the Epidemiology and Ecology of Infections
• Disease Agents, edited by Anderson and Thresh)
• p 262
• W.L. Liu and S.A. Levin Influenza and some related Mathematical Models p235
• H.W. Hethcote Rubella p 212
• in Applied Mathematical Ecology Eds
• S.A. Levin , Thomas Hallam and Louis Gross
• Biomathematic Texts
• Springer Verlag Berlin Heidelberg 1989
• 36. M. Turelli Random environments and stochastic calculus
• Theor. Pop. Biol. 12 (1977) 140-178
• 37. F. Solomon random walks in random environment
• ann prob 3 (1975) 1-31]
• 38 D. L. Soloman and C. Walter editors
• Mathematical Models in Biological Discovery
• Springer Verlag Berlin 1977
• 39. Harry Kesten Random Processes in Random Environments
• 82-92
• in
• Biological Growth and Spread
• W. Jager, H. Rost and P. Tautu
• Springer Verlag
• Lecture Notes in Biomathematics 38
• Heidelberg 1980
• See also
• 40. Y Ogura and H Kesten Recurrence properties
• of Lotka-Volterra models with Random Fluctuations J Math Soc
• Japan 32 (1981) 335
• 41. M. Turelli Stochastic Community Theory
• A Partial Guided Tour pp 321 -341
• L.M. Ricciardi Stochastic Population Theory:
• birth and death processes pp 155-190
• and
• Diffusion Processes p 191-240
• in Biomathematics Vol 17 Mathematical Ecology
• Ed TG Hallam and SA Levin
• Springer Verlag Berlin Heidelberg 1986
• SA Levin Random walk models of movement and their
• applications p 149-154
• Yu. M. Svirezhev and D.O. Logofet
• Stability of Mathematical Communities
• English Translation, Mir Publishers
• Moscow 1983.
• 42. A.S. Mikhailov Selected Topics in Fluctuational
• Kinetics of Reactions
• Physics Reports 184 No 5-6 (1989) 307-374
• North Holland Amsterdam
• Ya. B. Zeldovich Zh Tech Fiz 19 (1949) 1199
• Sov Electrochem 13 (1977) 581
• dokl akad nauk sssr 257 (1981) 1173
• S.F. Shandarin, A.G. Doroshkevich and Ya. B Zzeldovich
• Sov. Phys. Usp. 26 (1983) 46
• A.M. Gutin, A.S. Mikhailov and V.V. Yashin Sov. Phys.
• JETP 65 (1987) 535
• H.K. Janssen, Z. Phys. B 58 (1985) 311
• Ya. B. Zeldovich, S.A. Molchanov, A.A. Ruzmaikin and D.D. Sokoloff
• Proc. Nat. Acad. Sci. USA 84 (1987) 6323
• 43. Bruce J West
• An essay on the Importance of being Nonlinear
• Lecture Notes in Biomathematics 62
• Sspringer Verlag heidelberg 1985
• 44. W Horsthemke and R Lefever
• Noise Induced Transitions Theory and Applications
• in Physics Cemistry and Biology
• Springer Verlag Berlin Heidelberg 1984
• see also
• L. Arnold , W. Horsthemke and R Lefever
• White and colored external noise and transition phenomena
• in nonlinear systems Z Phys B 29 (1978) 867
• R.P. Garray , R. Lefever
• A kinetic approach to the immunology of cancer , stationary state properties
• of effector - target cell reactions
• J Theor Biology 73 (1978) 417.
• 45 P. Richmond, Power Law Distributions and Dynamic behaviour of Stock Markets, to appear in Eur.
• J. Phys 2001.
• 46.
• Mikhailov, Alexander S.
• Foundations of synergetics. I. Distributed active systems. 1st ed.
• Berlin, Springer-Verlag, 1990.
• Springer series in synergetics. v.51. [1st ed.]
• 47.
• Mikhailov, A.S. Loskutov, A.Yu.
• Foundations of synergetics. II. Complex patterns.
• Berlin, Springer-Verlag, 1991.
• Springer series in synergetics. v.52.

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