SciELO - Scientific Electronic Library Online

SciELO - Scientific Electronic Library Online

Referencias del artículo

CATSIGERAS, Eleonora. Deterministic dynamics and chaos: Epistemology and interdisciplinary methodology. Interdisciplinaria [online]. 2011, vol.28, n.2, pp. 279-298. ISSN 1668-7027.

    1. Anosov, D.V. (1962). Structural stability of geodesic flows on compact Riemannian manifolds of negative curvature. Dokl. Akad. Nauk. SSSR., 145, 707-709. [ Links ]

    2. Ayers, S. (1997). The application of chaos theory to psychology. Theory and Psychology, 7(3), 373-398. [ Links ]

    3. Budelli, R., Catsigeras, E., Enrich, H. & Torres, J. (1991). Two neuron network. Biological Cybernetics, 66, 95-101. [ Links ]

    4. Budelli, R. & Catsigeras, E. (1992). Limit cycles in a model of bineuronal networks. Physica D Nonlinear Phenomena, 56, 235-252. [ Links ]

    5. Budelli, R., Catsigeras, E., Rovella, A., Gómez, L. (1997). Dynamical behavior of pace-maker neurons networks. Journal of Nonlinear Analysis, 30(3), 1633-1638. [ Links ]

    6. Camacho, L. (2006). La lógica en Kant y en George Boole [The logic in Kant and in George Boole]. Revista de Filosofía de la Universidad de Costa Rica, 111-112, 49-56. [ Links ]

    7. Catsigeras, E. (2010). Chaos and stability in a model of inhibitory neuronal network. International Journal of Bifurcation and Chaos, 20(2), 349-360. [ Links ]

    8. Cessac, B. (2008). A discrete time neural network model with spiking. Journal of Mathematical Biology, 54, 311-345. [ Links ]

    9. Coombes, S. & Lord, G.J. (1997). De synchronization of pulse-coupled integrate-and-fire neurons. Physical Review E, 55(3), 2104-2017. [ Links ]

    10. Coombes, S. (2007). Mathematical neuroscience. Journal of Mathematical Biology, 54, 305-307. [ Links ]

    11. Coombes, S. & Laing, C.R. (2009). Delays in activity based neural networks. Philosophical Transactions of the Royal Society A, 367, 1117-1129. [ Links ]

    12. Cooper, L.N. (1995). How we learn. How we remember. Toward an understanding of brain and neural systems. Singapur: World Scientific. [ Links ]

    13. Eliasmith, C. (1996). The third contender: A critical examination of the dynamicist theory of cognition. Philosophical Psychology, 9(4), 441-463. [ Links ]

    14. Feudel, U., Neiman, A., Pei, X., Wojtenek, W., Braun, H., Huber, M. & Moss, F. (2000). Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons. Chaos. An Interdisciplinary Journal of Nonlinear Science, 10(231), 231-240. Retrieved November 24th., 2011 from http://chaos.aip.org/resource/1/chaoeh/v10/i1/p231_s1 [ Links ]

    15. Goldstein, J. (1995). The Tower of Babel in nonlinear dynamics: Toward the clarification of terms. In R. Robertson & A. Combs (Eds,), Chaos theory in Psychology and the life sciences (pp. 39-48). New Jersey: Erlbaum. [ Links ]

    16. Hodgkin, A.L. & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117(4), 500-544. [ Links ]

    17. Izhikevich, E. (2007). Dynamical systems in neuroscience: The geometry of excitability and bursting. Cambridge: MIT Press. [ Links ]

    18. Kellert, S.H (2008). Borrowed knowledge: Chaos theory and the challenge of learning across disciplines. Chicago & London. The University of Chicago Press. [ Links ]

    19. Kohonen,T. (1977). Associative memory: A system-theoretical approach. Berlin: Springer. [ Links ]

    20. Lamberti, P. & Rodríguez, V. (2007). Desarrollo del modelo matemático de Hodgkin y Huxley en neurociencias [Develpment of the mathematical model of Hodgkin and Huxley in neurosciences]. Revista Electroneurobiología, 15(4), 31-60. Retrieved Junio 21 2010 from http://electroneubio. secyt.gov.ar/ Lamberti-Rodriguez_Hodgkin-Huxley.htm [ Links ]

    21. Lansner, A. (2009). Associative memory models: From the cell-assembly theory to biophysically detailed cortex simulations. Trends in Neurosciences, 32(3), 78-186. [ Links ]

    22. Lewowicz, J. (1990). Expansive omeomorphisms of Surfaces. Boletim da Sociedade Brasileira de Matemática, 20(1), 113-133. [ Links ]

    23. Lewowicz, J. (2002). Acerca del caos [About chaos]. Actas de Fisiología, 8, 41-53. [ Links ]

    24. Lewowicz, J. (2008). Caos determinista y expansividad [Deterministic chaos and expansivity]. Anales de la Academia de Ciencias Exactas, Físicas y Naturales Argentina. Buenos Aires: Editorial de la ANCEFN. [ Links ]

    25. Lorenz, E. (1995). La esencia del caos [The essence of chaos]. Madrid: Editorial Debate. [ Links ]

    26. Mañé, R. (1987). Ergodic theory and differentiable dynamics. Berlin: Springer-Verlag. [ Links ]

    27. Markarian, R. & Gambini, R. (editors) (1997).Certidumbres. Incertidumbres. Caos. Reflexiones en torno a la ciencia contemporánea [Certainties. Uncertainties. Chaos. Reflexions around the contemporary science]. Montevideo: Ediciones Trilce. [ Links ]

    28. Massera, J.L. (1997). Reflexiones de un matemático sobre la dialéctica [Reflexions of a mathematician about the dialectic]. Prepublicaciones de Matemática de la Universidad de la República, Nº 97/01. [ Links ]

    29. Massera, J.L. (1988) Problemas de filosofía de la matemática, de sus fundamentos y metodología [Philosophical problems of the mathematics, its foundations and its methodology]. Publicaciones Matemáticas del Uruguay, 1,11-26. [ Links ]

    30. Mirollo, R. & Strogatz, S. (1990). Synchronization of pulse-coupled biological oscillators. SIAM Journal of Applied Mathematics, 50(6), 1645-1662. [ Links ]

    32. Mizraji, E.(2008). Neural memories and search engines. International Journal of General Systems, 37(6), 715-738. [ Links ]

    33. Mizraji, E. (2010). En busca de las leyes del pensamiento [In the search of the thinking laws]. Montevideo: Ediciones Trilce. [ Links ]

    34. Newhouse, S. (1979). The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms. Publications Mathématiques de L'IHÉS, 50(1), 101-151. [ Links ]

    35. Nowak, A. & Vallacher, R. (1998). Dynamical Social Psychology. New York: Guilford. [ Links ]

    36. Rieke, F., Warland, D., de Ruyter, R., Steveniorck, V. & Bialek, W. (1997). Spikes. Exploring the neural code. Cambridge: MIT Massachusetts Institute of Technology Press. [ Links ]

    37. Robertson, R. (1995). Chaos theory and the relationship between Psychology and science. In R. Robertson & A. Combs, (Eds.), Chaos theory in Psychology and the life sciences (pp. 3-16). New Jersey: Erlbaum. [ Links ]

    38. Ruelle, D. (1990). Deterministic chaos: The science and the fiction. Proceedings of the Royal Society of London A, 427, 241-248. [ Links ]

    39. Ruelle, D. (1993). Azar y caos [Chaos and hazard]. Madrid: Alianza. [ Links ]

    40. Rummens, S. & Cuypers, S. (2010). Determinism and the paradox of predictability. Erkenntnis, 72, 233-249. [ Links ]

    41. Scott, B. (1994). Chaos, self-organization, and Psychology. American Psychologist, 49(1), 5-14. [ Links ]

    42. Searle, J. (1978). Literal meaning. Erkenntnis, 13, 207-224. [ Links ]

    43. Sokal A. & Bricmont, J. (1999). Imposturas intelectuales [Intelectual impostures]. Barcelona: Paidós. [ Links ]

    44. Stewart, I. (1989). Does God play dice? The new Mathematics of chaos. London: Basil Blackwell. [ Links ]

    45. Strogatz, S.H. (1994). Non linear dynamics and chaos. With applications to Physics, Biology, Chemistry, and Engineering. Cambridge: Perseus Publshing. [ Links ]

    46. Timme, M., Wolf, F. & Geisel T. (2002). Co-existence of regular and irregular dynamicsin complex networks of pulse-coupled oscillators. Physical Review Letters, 89(25). Retrieved. November 9th., 2011, http://link.aps.org/doi/10.1103/PhysRevLett.89.258701 [ Links ]

    47. Vallacher, R. & Nowak, A. (1997). The emergence of dynamical Social Psychology. Psychological Inquiry, 8(2), 73-99. [ Links ]

    48. Vieitez, J.L. (1996). Expansive homeomorphisms and hyperbolic diffeomorphisms on 3-manifolds. Ergodic theory and dynamical systems, 16(3), 591-622. [ Links ]

    49. Von Neumann, J. (1958-posthumous). The computer and the brain. New Haven - London: Yale University Press. [ Links ]

    50. Yang, T. & Chua, L. (1997). Impulsive stabilization for control and synchronization of chaotic systems: Theory and application to secure communication. IEEE Transactions on circuits and systems E, 44(10), 976-988. [ Links ]

    51. Zollman, K. (2010). The epistemic benefit of transient diversity. Erkenntnis, 72, 17-35. [ Links ]