{"id":39569,"date":"2022-12-29T18:55:12","date_gmt":"2022-12-29T10:55:12","guid":{"rendered":"https:\/\/swarma.org\/?p=39569"},"modified":"2022-12-29T18:55:12","modified_gmt":"2022-12-29T10:55:12","slug":"%e6%b7%b7%e6%b2%8c%e9%a9%ac%e8%b9%84%e7%90%86%e8%ae%ba%e5%88%86%e6%9e%90%e5%8f%8a%e6%9e%84%e9%80%a0-%e9%9b%86%e6%99%ba%e8%af%be%e5%a0%82%c2%b7%e5%91%a8%e4%ba%94%e7%9b%b4%e6%92%ad","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=39569","title":{"rendered":"\u6df7\u6c8c\u9a6c\u8e44\u7406\u8bba\u5206\u6790\u53ca\u6784\u9020 | \u96c6\u667a\u8bfe\u5802\u00b7\u5468\u4e94\u76f4\u64ad"},"content":{"rendered":"
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20 \u4e16\u7eaa 70 \u5e74\u4ee3\u672b\u674e\u5929\u5ca9\u548c James Yorke \u5728\u6570\u5b66\u5206\u6790\u4e2d\u6b63\u5f0f\u5f15\u5165\u201c\u6df7\u6c8c\u201d\u8fd9\u4e2a\u79d1\u5b66\u672f\u8bed\u3002\u7ecf\u8fc7\u5b66\u672f\u754c\u4e2d\u597d\u51e0\u4ee3\u4eba\u8fd1 50 \u5e74\u7684\u5171\u540c\u52aa\u529b\uff0c\u6df7\u6c8c\u65e9\u5df2\u4e0d\u518d\u662f\u4e00\u4e2a\u964c\u751f\u7684\u6982\u5ff5\uff0c\u5176\u79d1\u5b66\u4f53\u7cfb\u65e5\u8d8b\u5b8c\u5584\uff0c\u5728\u6570\u5b66\u3001\u7269\u7406\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u3001\u751f\u547d\u79d1\u5b66\u3001\u793e\u4f1a\u79d1\u5b66\u3001\u5de5\u7a0b\u6280\u672f\u3001\u5546\u4e1a\u548c\u901a\u8baf\u7b49\u9886\u57df\u4e2d\u5f97\u5230\u4e86\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4e3a\u4e86\u5411\u8de8\u5b66\u79d1\u5b66\u4e60\u8005\u666e\u53ca\u6df7\u6c8c\u79d1\u5b66\u7684\u7406\u8bba\u77e5\u8bc6\uff0c\u96c6\u667a\u5b66\u56ed\u7279\u522b\u9080\u8bf7\u9648\u5173\u8363\u3001\u738b\u96c4\u3001\u674e\u6625\u5f6a\u3001\u5f20\u65ed\u3001\u9a6c\u519b\u3001\u5218\u575a\u3001\u738b\u9752\u4e91\u3001\u53f6\u56fd\u680b\u3001\u79b9\u601d\u654f9\u4f4d\u4ece\u4e8b\u6df7\u6c8c\u53ca\u76f8\u5173\u8de8\u5b66\u79d1\u7814\u7a76\u7684\u8d44\u6df1\u5b66\u8005\u62c5\u4efb\u5bfc\u5e08\uff0c\u5f00\u8bbe\u4e86\u300c<\/span><\/strong>\u6df7\u6c8c\u79d1\u5b66\u7cfb\u5217\u8bfe\u7a0b<\/span><\/strong><\/a>\u300d\u3002<\/span><\/strong><\/p>\n


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12\u670830\u65e5\uff08\u672c\u5468\u4e94\uff09\u665a19:00-21:30\uff0c\u5c06\u7531\u5c71\u4e1c\u5927\u5b66\uff08\u5a01\u6d77\uff09\u6570\u5b66\u4e0e\u7edf\u8ba1\u5b66\u9662\u6559\u6388\u3001\u535a\u58eb\u751f\u5bfc\u5e08\u5f20\u65ed\u8001\u5e08\u5f00\u542f\u6df7\u6c8c\u79d1\u5b66\u7b2c\u56db\u8bfe\uff0c\u56f4\u7ed5\u6df7\u6c8c\u52a8\u529b\u7cfb\u7edf\u7684\u91cd\u8981\u6a21\u578b Smale \u9a6c\u8e44\u5c55\u5f00\u3002\u4e3b\u8981\u5185\u5bb9\u5305\u62ec\u9a6c\u8e44\u53d1\u73b0\u7684\u6545\u4e8b\uff0c\u9a6c\u8e44\u6570\u5b66\u57fa\u7840\uff0c\u9a6c\u8e44\u7684\u52a8\u529b\u5b66\u884c\u4e3a\u63cf\u8ff0\uff0c\u4e00\u4e9b\u5177\u4f53\u6df7\u6c8c\u7cfb\u7edf\u4e2d\u9a6c\u8e44\u7684\u5206\u6790\u548c\u5e94\u7528\u3002<\/span><\/strong><\/p>\n

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\u53f2\u8482\u82ac\u00b7\u65af\u6885\u5c14 (Stephen Smale) \u6559\u6388\u662f\u4e00\u4f4d\u5bcc\u6709\u4f20\u5947\u8272\u5f69\u7684\u8457\u540d\u6570\u5b66\u5bb6\u3002\u5b66\u672f\u6210\u5c31\u548c\u751f\u6d3b\u8272\u5f69\u4e92\u4e3a\u8865\u5145\uff0c\u76f8\u8f85\u76f8\u6210\u3002\u65af\u6885\u5c14\u6559\u6388\u5728\u5fae\u5206\u62d3\u6251\u3001\u5fae\u5206\u52a8\u529b\u7cfb\u7edf\u3001\u6df7\u6c8c\u7406\u8bba\u3001\u5927\u8303\u56f4\u53d8\u5206\u5b66\u3001\u8ba1\u7b97\u590d\u6742\u6027\u3001\u6570\u7406\u7ecf\u6d4e\u5b66\u548c\u751f\u7269\u6570\u5b66\u7406\u8bba\u7b49\u4f17\u591a\u9886\u57df\uff0c\u90fd\u505a\u51fa\u4e86\u91cd\u8981\u8d21\u732e\u3002Smale \u9a6c\u8e44\u5c31\u662f\u4ed6\u5728\u5df4\u897f\u91cc\u7ea6\u70ed\u5185\u5362\u7684\u6d77\u6ee9\u4e0a\u7684\u91cd\u8981\u53d1\u73b0\uff0c\u4f5c\u4e3a\u6df7\u6c8c\u52a8\u529b\u7cfb\u7edf\u7684\u91cd\u8981\u6a21\u578b\u88ab\u5e94\u7528\u5230\u8bb8\u591a\u7cfb\u7edf\u7684\u590d\u6742\u52a8\u529b\u5b66\u884c\u4e3a\u7814\u7a76\u4e2d\u3002<\/strong><\/span><\/section>\n

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\u672c\u8bb2\u4e3b\u8981\u5185\u5bb9\u5305\u62ec\u9a6c\u8e44\u7684\u53d1\u73b0\uff0c\u9a6c\u8e44\u7684\u6570\u5b66\u57fa\u7840\u548c\u6784\u9020\uff0c\u9a6c\u8e44\u6df7\u6c8c\u52a8\u529b\u5b66\u884c\u4e3a\u7684\u7b26\u53f7\u63cf\u8ff0\uff0c\u4e00\u4e9b\u5177\u4f53\u6df7\u6c8c\u7cfb\u7edf\u4e2d\u9a6c\u8e44\u7684\u5206\u6790\u548c\u5e94\u7528\u3002\u6570\u5b66\u57fa\u7840\u4e3b\u8981\u8bb2\u8ff0\u5e73\u9762\u4e0a\u79bb\u6563\u7cfb\u7edf\uff0c\u79bb\u6563\u7cfb\u7edf\u53ef\u4ee5\u5e94\u7528\u5230\u8bb8\u591a\u5b9e\u9645\u95ee\u9898\u7814\u7a76\u4e2d\uff0c\u4f8b\u5982\u751f\u6001\u7cfb\u7edf\u4e2d\u5bbf\u4e3b\u5bc4\u751f\u866b\u6a21\u578b\u3001\u5e7f\u4e49 Lotka-Volterra \u79cd\u7fa4\u6a21\u578b\uff0c\u751f\u7269\u4e2d\u67d3\u8272\u4f53\u7b49\u4f4d\u57fa\u56e0\u9009\u62e9\u95ee\u9898\u3001\u4f20\u67d3\u75c5\u6a21\u578b\uff0c\u7ecf\u6d4e\u5b66\u4e2d\u7eb3\u4ec0\u5747\u8861\uff0c\u6570\u8bba\u95ee\u9898\uff0c\u795e\u7ecf\u5143\u7cfb\u7edf\u7b49\u3002\u9a6c\u8e44\u6784\u9020\u4e3b\u8981\u8bb2\u8ff0\u5728\u51e0\u7c7b\u7cfb\u7edf\u4e2d\u7684\u6784\u9020\uff0c\u5e76\u89e3\u91ca\u5176\u4e2d\u7684\u6df7\u6c8c\u52a8\u529b\u5b66\u542b\u4e49\u3002<\/span><\/strong><\/section>\n
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    \u9a6c\u8e44\u7684\u5386\u53f2<\/p>\n<\/li>\n

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    \u6570\u5b66\u57fa\u7840\u7b80\u4ecb<\/p>\n<\/li>\n

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    \u7cfb\u7edf\u4e2d\u7684\u9a6c\u8e44<\/p>\n<\/li>\n<\/ol>\n

    \u5173\u952e\u8bcd\uff1a<\/span><\/strong>\u79bb\u6563\u52a8\u529b\u5b66\u7cfb\u7edf\u3001\u674e-\u7ea6\u514b\u6df7\u6c8c\u3001Sharkovsky \u5e8f\u3001Collatz\u731c\u60f3\u3001H\u00e9non\u6620\u5c04\u3001\u4fdd\u9762\u79ef\u6620\u5c04\u3001\u62d3\u6251\u5171\u8f6d\u3001\u9a6c\u8e44\u6620\u5c04\u3001\u6b63\u5411\u8f68\u9053\u3001\u9006\u5411\u8f68\u9053\u3001\u7b26\u53f7\u52a8\u529b\u5b66\u3001\u9690\u85cf\u5438\u5f15\u5b50\u3001\u53cc\u500d\u5468\u671f\u5206\u5c94<\/span><\/section>\n
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    \u8bfe\u7a0b\u4e3b\u8bb2\u4eba<\/strong><\/strong><\/p>\n<\/section>\n

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    <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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    \u5f20\u65ed<\/span><\/strong>\uff0c\u5c71\u4e1c\u5927\u5b66\uff08\u5a01\u6d77\uff09\uff0c\u6570\u5b66\u4e0e\u7edf\u8ba1\u5b66\u9662\u6559\u6388\uff0c\u7f8e\u56fd\u300a\u6570\u5b66\u8bc4\u8bba\u300b\u4e0e\u5fb7\u56fd\u300a\u6570\u5b66\u6587\u6458\u300b\u8bc4\u8bba\u5458\u3002\u5728 Chaos, Chaos Solitons and Fractals, Discrete and Continuous Dynamical Systems, Ergodic Theory and Dynamical Systems, Fuzzy Sets and Systems,IEEE Transactions on Fuzzy Systems,International Journal of Bifurcation and Chaos, Proceedings of the American Mathematical Society \u7b49\u6742\u5fd7\u53d1\u8868 SCI \u8bba\u6587\u591a\u7bc7\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u53c2\u8003\u6587\u732e\uff08\u6309\u8bfe\u7a0b\u4e3b\u9898\u987a\u5e8f\u6392\u5217\uff09\uff1a<\/span><\/strong><\/span><\/section>\n
    \u9a6c\u8e44\u7684\u5386\u53f2<\/span><\/strong><\/section>\n

    1. van der Pol\uff0cJ. van der Mark\uff1bFrequency demultiplication, Nature, 1927.<\/span><\/p>\n

    2. S. L. McMurran, J. J. Tattersall; The mathematical collaboration of M L Cartwright and J E Littlewood, Amer. Math. Monthly, 1996.<\/span><\/p>\n

    3. S. L. McMurran, J. J. Tattersall; Cartwright and Littlewood on van der Pol\u2019s equation, in Harmonic analysis and nonlinear differential equations, Riverside, CA, 1995, Contemp. Math. 208, Providence, RI, 1997.<\/span><\/p>\n

    4. S. Smale; On the steps of Moscow University. From Topology to Computation: Proceedings of the Smalefest (Berkeley, CA, 1990), 41-52, Springer, New York, 1993.<\/span><\/p>\n

    5. S. Smale; Finding a horseshoe on the beaches of Rio, The Mathematical Intelligencer, 1998.<\/span><\/p>\n

    6. https:\/\/math.berkeley.edu\/~smale\/<\/span><\/p>\n

    \u6570\u5b66\u57fa\u7840<\/span><\/strong><\/section>\n

    7. Y. Li J. Yorke\uff1bPeriod three implies chaos, 1975.<\/span><\/p>\n

    8. R. Mays; Simple mathematical models with very complicated dynamics, Nature, 1976.<\/span><\/p>\n

    9. R. Devaney; An Introduction to Chaotic Dynamical Systems, 1987.<\/span><\/p>\n

    10. M. W. Hirsch, S. Smale, R. L. Devaney; Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2013.<\/span><\/p>\n

    \u7cfb\u7edf\u4e2d\u7684\u9a6c\u8e44<\/span><\/strong><\/section>\n

    11. R. L.Devaney, Z. Nitecki; Shift automorphisms in the Henon mapping, Comm. Math. Phys., 1979.<\/span><\/p>\n

    12. X. Zhang, G. Chen; Polynomial maps with hidden complex dynamics, Discrete and Continuous Dynamical Systems-B, 2019.<\/span><\/p>\n

    13. X. Zhang, G. Chen; A simple topological model for two coupled neurons, Chaos, 2022.<\/span><\/p>\n

    \u5bbf\u4e3b\u5bc4\u751f\u866b\u6a21\u578b<\/span><\/strong><\/section>\n

    14. R. M. May;  Host-parasitoid systems in patchy environments: a phenomenological model, J. Animal Ecol., 1978.<\/span><\/p>\n

    15. R. M. May,  M. P. Hassell; The dynamics of multiparasitoid-host interactions, The American Naturalist, 1981.<\/span><\/p>\n

    \u5e7f\u4e49 L-V \u4e24\u79cd\u7fa4\u6a21\u578b<\/span><\/strong><\/section>\n

    16. R. M. May; Biological populations with nonoverlapping generations: stable points, stable cycles and chaos, Science, 1974.<\/span><\/p>\n

    17. H. Jiang, T. D. Rogers; The discrete dynamics of symmetric competition in the plane, J. Math. Biol., 1987.<\/span><\/p>\n

    \u67d3\u8272\u4f53\u540c\u4e00\u4f4d\u7f6e\u4e0a\u7684\u4e24\u5bf9\u7b49\u4f4d\u57fa\u56e0\u7684\u9009\u62e9\u95ee\u9898<\/span><\/strong><\/section>\n

    18. J. F. Selgrade,  M. Ziehe; Convergence to equilibrium in a genetic model with differential viability between the sexes, J. Math. Biol., 1987.<\/span><\/p>\n

    \u540c\u4e00\u7247\u571f\u5730\u4e0a\u4e24\u79cd\u7ebf\u866b\u7684\u7ade\u4e89\u95ee\u9898<\/span><\/strong><\/span><\/section>\n

    19. F. Jones, J. Perry; Modelling populations of cyst-nematodes (nematoda: heteroderidae), J. Appl. Ecology, 1978.<\/span><\/p>\n

    \u4f20\u67d3\u75c5\u6a21\u578b<\/span><\/strong><\/section>\n

    20. L. Allen; Some discrete-time SI, SIS, and SIR epidemic models, Math. Biosciences, 1994.<\/span><\/p>\n

    21. L.  Allen, A. B. Burgin; Comparison of deterministic and stochastic SIS and SIR models in discrete time, Math. Biosciences, 2000.<\/span><\/p>\n

    \u7ecf\u6d4e\u5b66\u4e2d\u7684\u5e94\u7528<\/span><\/strong><\/section>\n
      \n
    1. \n
      A. Cournot; Recherche sur la Principes Matematiques de la Theorie de la Richesse, Hachette, Paris, 1838.<\/span><\/section>\n<\/li>\n<\/ol>\n
      \u795e\u7ecf\u79d1\u5b66\u4e2d\u7684\u5e94\u7528<\/span><\/strong><\/section>\n

      23. A. L. Hodgkin, A. F. Huxley; A quantitative description of membrane current and its applications to conduction and excitation in nerve, J. Physiol. (Lond.), 1952.<\/span><\/p>\n

      24. J. Guckenheimer, R. A. Oliva; Chaos in the Hodgkin-Huxley model, SIAM J. Appl. Dyn. Syst., 2002.<\/span><\/p>\n

      25. W. Gerstner, W. M. Kistler, R. Naud, L. Paninski; Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge Univ. Press, Cambridge, 2014.<\/span><\/p>\n

      26. M. A. Arbib, editor. The Handbook of Brain Theory and Neural Networks-2nd ed. The MIT Press, Cambridge, 2003.<\/span><\/p>\n

      27. K. Aihara, T. Takabe, M. Toyoda; Chaotic neural networks. Physics Letters A, 1990.<\/span><\/p>\n


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      12\u670830\u65e5\uff08\u5468\u4e94\uff09 19:00-21:30<\/span><\/p>\n

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