1887
  1. Home
  2. Books
  3. Second Language Acquisition Theory
  4. Chapter

Chapter 3. Stabilization

A dynamic account

image of Chapter 3. Stabilization

We accord with Mike Long’s rejection of fossilization as a concept able to describe or explain second language acquisition. And we share his bewilderment (Long, 2003, p. 512f.) that since most studies of fossilization make reference to explanatory factors external to language and cognition, “[s]urprisingly, no one seems to have considered the possibility that if fossilization is, as Selinker (1972) claimed, a cognitive mechanism producing the non-target end-state also called ‘fossilization’, there is no need for other explanations …”. In this paper we take up Mike’s proposition that stabilization might be a more viable alternative to fossilization and propose exactly what Mike asked for, a cognitive mechanism. We demonstrate that in SLA, linguistic simplification, one aspect of stabilization, is a dynamic process that follows its own regularities. We show that it can be modeled in an AI simulation of SLA using the mathematical formalisms of dynamical systems theory that are implied in agent-based modeling. In doing this we show that the formal, mathematical architecture of dynamical systems theory is particularly well suited for a simulation of the cognitive stabilisation mechanism that Mike Long asked for, because agent-based modeling can operate entirely on the basis of the internal dynamics of identifiable stabilization mechanisms, and they can lead to tipping points at which the system may abruptly change direction. Differing from the postmodern DST metaphors that are currently popular among some applied linguists (e.g., Larsen-Freeman, 2006), we have followed Long’s (2003) call for an operationalized concept that is testable. In this chapter, our agent-based model is fully operationalized and tested against longitudinal empirical data. Our chapter spans a period of four decades during which the first author and Mike interacted. Many of these interactions left traces in the research described here. Contextualising this research in its ‘historical’ background may be helpful in tracing the development of ideas that lead up to the AI simulation of SLA reported in this chapter. As the reader will see, many of these ideas were intentionally or unintentionally inspired or provoked by Mike’s critique, comments, suggestions and the presence of his critical mind.

  • Affiliations: 1: Paderborn University/Linguistic Engineering Co.; 2: Linguistic Engineering Co.; 3: La Trobe University; 4: Innsbruck University

References

  1. Bailey, C.-J.
    (1973) Variation and linguistic theory. Center for Applied Linguistics.
     [Google Scholar]
  2. Bickerton, D.
    (1971) Inherent variability and variable rules. Foundations of Language, 7 , 457–492.
     [Google Scholar]
  3. Borshchev, B. , & Filippov, A.
    (2004) From system dynamics and discrete event to practical agent based modeling: Reasons, techniques, tools. The 22nd International Conference of the System Dynamics Society, 25–29 July 25, Oxford, England.
     [Google Scholar]
  4. Bresnan, J.
    (2001) Lexical-functional syntax. Blackwell.
     [Google Scholar]
  5. Clahsen, H. , Meisel, J. M. , & Pienemann, M.
    (1983) Deutsch als Zweitsprache. Der Zweitspracherwerb ausländischer Arbeiter [German as a second language. The second language acquisition of immigrant workers]. Gunter Narr.
     [Google Scholar]
  6. Clyne, M.
    (Ed.) (1981) Foreigner talk. International Journal of the Sociology of Language, 28 .
     [Google Scholar]
  7. De Bot, K.
    (2016) Multi-competence and dynamic systems. In V. Cook & Li Wei (Eds.), The Cambridge handbook of linguistic multi-competence (pp.125–141). Cambridge University Press. 10.1017/CBO9781107425965.006
     https://doi.org/10.1017/CBO9781107425965.006 [Google Scholar]
  8. De Bot, K. , Lowie, W. M. , & Verspoor, M. H.
    (2007) A dynamic systems theory approach to second language acquisition. Bilingualism: Language and Cognition, 10 (1), 7–21. 10.1017/S1366728906002732
     https://doi.org/10.1017/S1366728906002732 [Google Scholar]
  9. DeCamp, D.
    (1973) What do implicational scales imply?In C.-J. N. Bailey & R. W. Shuy (Eds.), New ways of analyzing variation in English (pp.141–148). Georgetown University Press.
     [Google Scholar]
  10. Dyson, B. P.
    (2021) Dynamic variation in second language acquisition. A language processing perspective. John Benjamins. 10.1075/palart.8
     https://doi.org/10.1075/palart.8 [Google Scholar]
  11. Ebbinghaus, H.
    (1885)  Über das Gedächtnis: Untersuchungen zur experimentellen Psychologie. Duncker & Humblot. English translation: Memory: A contribution to experimental psychology. Columbia University 1913.
     [Google Scholar]
  12. Feldman, D. P.
    (2012) Chaos and fractals. An elementary introduction. Oxford University Press. 10.1093/acprof:oso/9780199566433.001.0001
     https://doi.org/10.1093/acprof:oso/9780199566433.001.0001 [Google Scholar]
  13. (2019) Chaos and dynamical systems. Princeton University Press.
     [Google Scholar]
  14. Hakuta, K.
    (1974) Learning to speak a second language: What exactly does the child learn?In D. Dato (ed.), Georgetown University round table on languages and linguistics 1975 (pp.193–207). Georgetown University Press.
     [Google Scholar]
  15. Han, Z. H.
    (2004) Fossilisation in adult second language acquisition. Multilingual Matters. 10.21832/9781853596889
     https://doi.org/10.21832/9781853596889 [Google Scholar]
  16. Hatch, E. , & Lazaraton, A.
    (1991) The research manual. Design and statistics for applied linguists. Heinle and Heinle.
     [Google Scholar]
  17. Haznedar, B.
    (1997) Child second language acquisition of English: A longitudinal case study of a Turkish-speaking child (Unpublished doctoral dissertation). Durham University.
  18. Hyltenstam, K. , & Abrahamsson, N.
    (2003) Maturaltional constraints in SLA. In C. Doughty & M. Long (Eds.), The handbook of second language acquisition research (pp.539–587). Blackwell. 10.1002/9780470756492.ch17
     https://doi.org/10.1002/9780470756492.ch17 [Google Scholar]
  19. Kempen, G. , & Hoenkamp, E.
    (1987) An incremental procedural grammar for sentence formulation. Cognitive Science, 11 , 201–258. 10.1207/s15516709cog1102_5
     https://doi.org/10.1207/s15516709cog1102_5 [Google Scholar]
  20. Labov, W.
    (1972) Sociolinguistic patterns. University of Pennsylvania Press.
     [Google Scholar]
  21. Larsen-Freeman, D.
    (2006) The emergence of complexity, fluency, and accuracy in the oral and written production of five Chinese learners of English. Applied Linguistics, 27 (4), 590–619. 10.1093/applin/aml029
     https://doi.org/10.1093/applin/aml029 [Google Scholar]
  22. Larsen-Freemann, D. , & Long, M. H.
    (1991) An introduction to second language acquisition research. Longman.
     [Google Scholar]
  23. Lenzing, A. , Nicholas, H. , & Roos, J.
    (Eds.) (2019) Widening contexts for Processability Theory: Theories and issues. John Benjamins. 10.1075/palart.7
     https://doi.org/10.1075/palart.7 [Google Scholar]
  24. Lenzing, A. , Pienemann, M. , & Nicholas, H.
    (2022) Lost in translation? On some key features of dynamical systems theorizing invoked in SLA research. In K. Kersten & A. Winsler (Eds) Understanding variability in second language acquisition, bilingualism and cognition. Routledge.
     [Google Scholar]
  25. Li, T-Y. , & Yorke, J.
    (1975) Period three implies chaos. The American Mathematical Monthly, 82 (10), 985–992. 10.1080/00029890.1975.11994008
     https://doi.org/10.1080/00029890.1975.11994008 [Google Scholar]
  26. Long, M. H.
    (2003) Stabilization and fossilization. In C. Doughty & M. Long (Eds.), The handbook of second language acquisition research (pp.487–536). Blackwell. 10.1002/9780470756492.ch16
     https://doi.org/10.1002/9780470756492.ch16 [Google Scholar]
  27. May, R. M.
    (1976) Simple mathematical models with very complicated dynamics. Nature, 261 (5560), 459–467. 10.1038/261459a0
     https://doi.org/10.1038/261459a0 [Google Scholar]
  28. Meisel, J. M. , Clahsen, H. , & Pienemann, M.
    (1981) On determining developmental stages in second language acquisition. Studies in Second Language Acquisition, 3 (2), 109–135. 10.1017/S0272263100004137
     https://doi.org/10.1017/S0272263100004137 [Google Scholar]
  29. Meisel, J. M.
    (2011) First and second language acquisition. Cambridge University Press. 10.1017/CBO9780511862694
     https://doi.org/10.1017/CBO9780511862694 [Google Scholar]
  30. Mitchell, M.
    (2009) Complexity. A guided tour. Oxford University Press.
     [Google Scholar]
  31. Nash, J. E. , & Sutcliffe, J. V.
    (1970) River flow forecasting through conceptual models part I – A discussion of principles. Journal of Hydrology, 10 (3), 282–290. 10.1016/0022‑1694(70)90255‑6
     https://doi.org/10.1016/0022-1694(70)90255-6 [Google Scholar]
  32. Nicholas, H.
    (1987) A comparative study of the acquisition of German as a first and as a second language (Unpublished doctoral dissertation). Monash University. Retrieved on2 February 2022fromhttps://monash.hosted.exlibrisgroup.com/MON:au_everything:catau21186631810001751
  33. Nicholas, H. , Lenzing, A. , & Roos, J.
    (2019) How does PT’s view of acquisition relate to the challenge of widening perspectives on SLA?In A. Lenzing , H. Nicholas , & J. Roos (Eds.), Widening contexts for Processability Theory: Theories and issues (pp.391–398). John Benjamins. 10.1075/palart.7.17nic
     https://doi.org/10.1075/palart.7.17nic [Google Scholar]
  34. Pienemann, M.
    (1980) The second language acquisition of immigrant children. In S. W. Felix (Ed.), Second language development. Trends and issues (pp.41–56). Narr.
     [Google Scholar]
  35. (1981) Der Zweitspracherwerb ausländischer Arbeiterkinder [The second language acquisition of immigrant children]. Bonn: Bouvier.
     [Google Scholar]
  36. (1998) Language processing and second language development: Processability Theory. John Benjamins. 10.1075/sibil.15
     https://doi.org/10.1075/sibil.15 [Google Scholar]
  37. (2005) (ed.) Cross-Linguistic Aspects of Processability Theory. John Benjamins: Amsterdam.
     [Google Scholar]
  38. (2011) The psycholinguistic basis of PT. In M. Pienemann & J.-U. Keßler (Eds.), Studying Processability Theory (pp.27–49). John Benjamins. 10.1075/palart.1.03the
     https://doi.org/10.1075/palart.1.03the [Google Scholar]
  39. (2015) An outline of processability theory and its relationship to other approaches to SLA. Language Learning, 65 (1), 123–151. 10.1111/lang.12095
     https://doi.org/10.1111/lang.12095 [Google Scholar]
  40. Pienemann, M. , Johnston, M. , & Brindley, G.
    (1988) Constructing an acquisition-based procedure for second language assessment. Studies in Second Language Acquisition, 10 , 217–243. 10.1017/S0272263100007324
     https://doi.org/10.1017/S0272263100007324 [Google Scholar]
  41. Pienemann, M. , & Lenzing, A.
    (2020) Processability Theory. In B. VanPatten , G. D. Keating , & S. Wulff (Eds.), Theories in second language acquisition. An introduction (3rd ed., pp.162–191). Routledge. 10.4324/9780429503986‑8
     https://doi.org/10.4324/9780429503986-8 [Google Scholar]
  42. Pienemann, M. , Lenzing, A. , & Nicholas, H.
    (forthcoming). Can dynamic systems theory explain SLA?Unpublished manuscript, University of Paderborn, Germany.
     [Google Scholar]
  43. Poincaré, J. H.
    (1913) The foundations of science: Vol 1, Science and hypothesis; Vol II, The value of science; Vol III, Science and method ( G. Halsted , Trans.). The Science Press. (Original works published in 1902 (Vol I), 1905 (Vol II), 1908 (Vol III)).
     [Google Scholar]
  44. Rasmussen, N.
    (1987) A new model of developmental constraints as applied to the Drosophila system. Journal of Theoretical Biology, 127 (3), 271–299. PMID:3431126. 10.1016/S0022‑5193(87)80107‑8
     https://doi.org/10.1016/S0022-5193(87)80107-8 [Google Scholar]
  45. Scheffer, M.
    (2010) Foreseeing tipping points. Nature, 467, 411–412. 10.1038/467411a
     https://doi.org/10.1038/467411a [Google Scholar]
  46. Selinker, L.
    (1972) Interlanguage. IRAL, 10 , 209–231. 10.1515/iral.1972.10.1‑4.209
     https://doi.org/10.1515/iral.1972.10.1-4.209 [Google Scholar]
  47. Simon, H. A.
    (1962) The architecture of complexity. Proceedings of the American Philosophical Society, 106 , 467–482.
     [Google Scholar]
  48. Strogatz, S. H.
    (2015) Nonlinear dynamics and chaos. With applications to physics, biology, chemistry and engineering (2nd ed.). Westview.
     [Google Scholar]
  49. Verhulst, P.-F.
    (1838) Notice sur la loi que la population poursuit dans son accroissement. Correspondance Mathématique et Physique, 10 , 113–121. (cited after Nicolas Bacaër 2011).
     [Google Scholar]
  50. Watkins, C. , Massey, D. , Brooks, J. , Ross, K. , & Zellner, M. L.
    (2013) Understanding the mechanisms of collective decision making in ecological restoration: An agent-based model of actors and organizations. Ecology and Society, 18 (2), 32. 10.5751/ES‑05497‑180232
     https://doi.org/10.5751/ES-05497-180232 [Google Scholar]
  51. Wilensky, U.
    (1999) NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. Retrieved on2 February 2022fromccl.northwestern.edu/netlogo/
     [Google Scholar]
  52. Wimsatt, W.
    (1986) Developmental constraints, generative entrenchment and the innate-acquired distinction. In W. Bechtel . (ed.), Integrating scientific disciplines (pp.185–208). Martinus Nijhoff. 10.1007/978‑94‑010‑9435‑1_11
     https://doi.org/10.1007/978-94-010-9435-1_11 [Google Scholar]

References

  1. Bailey, C.-J.
    (1973) Variation and linguistic theory. Center for Applied Linguistics.
     [Google Scholar]
  2. Bickerton, D.
    (1971) Inherent variability and variable rules. Foundations of Language, 7 , 457–492.
     [Google Scholar]
  3. Borshchev, B. , & Filippov, A.
    (2004) From system dynamics and discrete event to practical agent based modeling: Reasons, techniques, tools. The 22nd International Conference of the System Dynamics Society, 25–29 July 25, Oxford, England.
     [Google Scholar]
  4. Bresnan, J.
    (2001) Lexical-functional syntax. Blackwell.
     [Google Scholar]
  5. Clahsen, H. , Meisel, J. M. , & Pienemann, M.
    (1983) Deutsch als Zweitsprache. Der Zweitspracherwerb ausländischer Arbeiter [German as a second language. The second language acquisition of immigrant workers]. Gunter Narr.
     [Google Scholar]
  6. Clyne, M.
    (Ed.) (1981) Foreigner talk. International Journal of the Sociology of Language, 28 .
     [Google Scholar]
  7. De Bot, K.
    (2016) Multi-competence and dynamic systems. In V. Cook & Li Wei (Eds.), The Cambridge handbook of linguistic multi-competence (pp.125–141). Cambridge University Press. 10.1017/CBO9781107425965.006
     https://doi.org/10.1017/CBO9781107425965.006 [Google Scholar]
  8. De Bot, K. , Lowie, W. M. , & Verspoor, M. H.
    (2007) A dynamic systems theory approach to second language acquisition. Bilingualism: Language and Cognition, 10 (1), 7–21. 10.1017/S1366728906002732
     https://doi.org/10.1017/S1366728906002732 [Google Scholar]
  9. DeCamp, D.
    (1973) What do implicational scales imply?In C.-J. N. Bailey & R. W. Shuy (Eds.), New ways of analyzing variation in English (pp.141–148). Georgetown University Press.
     [Google Scholar]
  10. Dyson, B. P.
    (2021) Dynamic variation in second language acquisition. A language processing perspective. John Benjamins. 10.1075/palart.8
     https://doi.org/10.1075/palart.8 [Google Scholar]
  11. Ebbinghaus, H.
    (1885)  Über das Gedächtnis: Untersuchungen zur experimentellen Psychologie. Duncker & Humblot. English translation: Memory: A contribution to experimental psychology. Columbia University 1913.
     [Google Scholar]
  12. Feldman, D. P.
    (2012) Chaos and fractals. An elementary introduction. Oxford University Press. 10.1093/acprof:oso/9780199566433.001.0001
     https://doi.org/10.1093/acprof:oso/9780199566433.001.0001 [Google Scholar]
  13. (2019) Chaos and dynamical systems. Princeton University Press.
     [Google Scholar]
  14. Hakuta, K.
    (1974) Learning to speak a second language: What exactly does the child learn?In D. Dato (ed.), Georgetown University round table on languages and linguistics 1975 (pp.193–207). Georgetown University Press.
     [Google Scholar]
  15. Han, Z. H.
    (2004) Fossilisation in adult second language acquisition. Multilingual Matters. 10.21832/9781853596889
     https://doi.org/10.21832/9781853596889 [Google Scholar]
  16. Hatch, E. , & Lazaraton, A.
    (1991) The research manual. Design and statistics for applied linguists. Heinle and Heinle.
     [Google Scholar]
  17. Haznedar, B.
    (1997) Child second language acquisition of English: A longitudinal case study of a Turkish-speaking child (Unpublished doctoral dissertation). Durham University.
  18. Hyltenstam, K. , & Abrahamsson, N.
    (2003) Maturaltional constraints in SLA. In C. Doughty & M. Long (Eds.), The handbook of second language acquisition research (pp.539–587). Blackwell. 10.1002/9780470756492.ch17
     https://doi.org/10.1002/9780470756492.ch17 [Google Scholar]
  19. Kempen, G. , & Hoenkamp, E.
    (1987) An incremental procedural grammar for sentence formulation. Cognitive Science, 11 , 201–258. 10.1207/s15516709cog1102_5
     https://doi.org/10.1207/s15516709cog1102_5 [Google Scholar]
  20. Labov, W.
    (1972) Sociolinguistic patterns. University of Pennsylvania Press.
     [Google Scholar]
  21. Larsen-Freeman, D.
    (2006) The emergence of complexity, fluency, and accuracy in the oral and written production of five Chinese learners of English. Applied Linguistics, 27 (4), 590–619. 10.1093/applin/aml029
     https://doi.org/10.1093/applin/aml029 [Google Scholar]
  22. Larsen-Freemann, D. , & Long, M. H.
    (1991) An introduction to second language acquisition research. Longman.
     [Google Scholar]
  23. Lenzing, A. , Nicholas, H. , & Roos, J.
    (Eds.) (2019) Widening contexts for Processability Theory: Theories and issues. John Benjamins. 10.1075/palart.7
     https://doi.org/10.1075/palart.7 [Google Scholar]
  24. Lenzing, A. , Pienemann, M. , & Nicholas, H.
    (2022) Lost in translation? On some key features of dynamical systems theorizing invoked in SLA research. In K. Kersten & A. Winsler (Eds) Understanding variability in second language acquisition, bilingualism and cognition. Routledge.
     [Google Scholar]
  25. Li, T-Y. , & Yorke, J.
    (1975) Period three implies chaos. The American Mathematical Monthly, 82 (10), 985–992. 10.1080/00029890.1975.11994008
     https://doi.org/10.1080/00029890.1975.11994008 [Google Scholar]
  26. Long, M. H.
    (2003) Stabilization and fossilization. In C. Doughty & M. Long (Eds.), The handbook of second language acquisition research (pp.487–536). Blackwell. 10.1002/9780470756492.ch16
     https://doi.org/10.1002/9780470756492.ch16 [Google Scholar]
  27. May, R. M.
    (1976) Simple mathematical models with very complicated dynamics. Nature, 261 (5560), 459–467. 10.1038/261459a0
     https://doi.org/10.1038/261459a0 [Google Scholar]
  28. Meisel, J. M. , Clahsen, H. , & Pienemann, M.
    (1981) On determining developmental stages in second language acquisition. Studies in Second Language Acquisition, 3 (2), 109–135. 10.1017/S0272263100004137
     https://doi.org/10.1017/S0272263100004137 [Google Scholar]
  29. Meisel, J. M.
    (2011) First and second language acquisition. Cambridge University Press. 10.1017/CBO9780511862694
     https://doi.org/10.1017/CBO9780511862694 [Google Scholar]
  30. Mitchell, M.
    (2009) Complexity. A guided tour. Oxford University Press.
     [Google Scholar]
  31. Nash, J. E. , & Sutcliffe, J. V.
    (1970) River flow forecasting through conceptual models part I – A discussion of principles. Journal of Hydrology, 10 (3), 282–290. 10.1016/0022‑1694(70)90255‑6
     https://doi.org/10.1016/0022-1694(70)90255-6 [Google Scholar]
  32. Nicholas, H.
    (1987) A comparative study of the acquisition of German as a first and as a second language (Unpublished doctoral dissertation). Monash University. Retrieved on2 February 2022fromhttps://monash.hosted.exlibrisgroup.com/MON:au_everything:catau21186631810001751
  33. Nicholas, H. , Lenzing, A. , & Roos, J.
    (2019) How does PT’s view of acquisition relate to the challenge of widening perspectives on SLA?In A. Lenzing , H. Nicholas , & J. Roos (Eds.), Widening contexts for Processability Theory: Theories and issues (pp.391–398). John Benjamins. 10.1075/palart.7.17nic
     https://doi.org/10.1075/palart.7.17nic [Google Scholar]
  34. Pienemann, M.
    (1980) The second language acquisition of immigrant children. In S. W. Felix (Ed.), Second language development. Trends and issues (pp.41–56). Narr.
     [Google Scholar]
  35. (1981) Der Zweitspracherwerb ausländischer Arbeiterkinder [The second language acquisition of immigrant children]. Bonn: Bouvier.
     [Google Scholar]
  36. (1998) Language processing and second language development: Processability Theory. John Benjamins. 10.1075/sibil.15
     https://doi.org/10.1075/sibil.15 [Google Scholar]
  37. (2005) (ed.) Cross-Linguistic Aspects of Processability Theory. John Benjamins: Amsterdam.
     [Google Scholar]
  38. (2011) The psycholinguistic basis of PT. In M. Pienemann & J.-U. Keßler (Eds.), Studying Processability Theory (pp.27–49). John Benjamins. 10.1075/palart.1.03the
     https://doi.org/10.1075/palart.1.03the [Google Scholar]
  39. (2015) An outline of processability theory and its relationship to other approaches to SLA. Language Learning, 65 (1), 123–151. 10.1111/lang.12095
     https://doi.org/10.1111/lang.12095 [Google Scholar]
  40. Pienemann, M. , Johnston, M. , & Brindley, G.
    (1988) Constructing an acquisition-based procedure for second language assessment. Studies in Second Language Acquisition, 10 , 217–243. 10.1017/S0272263100007324
     https://doi.org/10.1017/S0272263100007324 [Google Scholar]
  41. Pienemann, M. , & Lenzing, A.
    (2020) Processability Theory. In B. VanPatten , G. D. Keating , & S. Wulff (Eds.), Theories in second language acquisition. An introduction (3rd ed., pp.162–191). Routledge. 10.4324/9780429503986‑8
     https://doi.org/10.4324/9780429503986-8 [Google Scholar]
  42. Pienemann, M. , Lenzing, A. , & Nicholas, H.
    (forthcoming). Can dynamic systems theory explain SLA?Unpublished manuscript, University of Paderborn, Germany.
     [Google Scholar]
  43. Poincaré, J. H.
    (1913) The foundations of science: Vol 1, Science and hypothesis; Vol II, The value of science; Vol III, Science and method ( G. Halsted , Trans.). The Science Press. (Original works published in 1902 (Vol I), 1905 (Vol II), 1908 (Vol III)).
     [Google Scholar]
  44. Rasmussen, N.
    (1987) A new model of developmental constraints as applied to the Drosophila system. Journal of Theoretical Biology, 127 (3), 271–299. PMID:3431126. 10.1016/S0022‑5193(87)80107‑8
     https://doi.org/10.1016/S0022-5193(87)80107-8 [Google Scholar]
  45. Scheffer, M.
    (2010) Foreseeing tipping points. Nature, 467, 411–412. 10.1038/467411a
     https://doi.org/10.1038/467411a [Google Scholar]
  46. Selinker, L.
    (1972) Interlanguage. IRAL, 10 , 209–231. 10.1515/iral.1972.10.1‑4.209
     https://doi.org/10.1515/iral.1972.10.1-4.209 [Google Scholar]
  47. Simon, H. A.
    (1962) The architecture of complexity. Proceedings of the American Philosophical Society, 106 , 467–482.
     [Google Scholar]
  48. Strogatz, S. H.
    (2015) Nonlinear dynamics and chaos. With applications to physics, biology, chemistry and engineering (2nd ed.). Westview.
     [Google Scholar]
  49. Verhulst, P.-F.
    (1838) Notice sur la loi que la population poursuit dans son accroissement. Correspondance Mathématique et Physique, 10 , 113–121. (cited after Nicolas Bacaër 2011).
     [Google Scholar]
  50. Watkins, C. , Massey, D. , Brooks, J. , Ross, K. , & Zellner, M. L.
    (2013) Understanding the mechanisms of collective decision making in ecological restoration: An agent-based model of actors and organizations. Ecology and Society, 18 (2), 32. 10.5751/ES‑05497‑180232
     https://doi.org/10.5751/ES-05497-180232 [Google Scholar]
  51. Wilensky, U.
    (1999) NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. Retrieved on2 February 2022fromccl.northwestern.edu/netlogo/
     [Google Scholar]
  52. Wimsatt, W.
    (1986) Developmental constraints, generative entrenchment and the innate-acquired distinction. In W. Bechtel . (ed.), Integrating scientific disciplines (pp.185–208). Martinus Nijhoff. 10.1007/978‑94‑010‑9435‑1_11
     https://doi.org/10.1007/978-94-010-9435-1_11 [Google Scholar]

  • From This Site

    /content/books/9789027257482-bpa.14.03pie
    dcterms_subject,pub_keyword
    -contentType:Journal
    10
    5
/content/books/9789027257482-bpa.14.03pie
dcterms_subject,pub_keyword
-contentType:Journal
10
5
Chapter
content/books/9789027257482
Book
false
Loading
This is a required field
Please enter a valid email address
Approval was successful
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error