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National Chair-Professor, Ministry of Education Song-Sun Lin

Contact
  • Email: sslin@math.nctu.edu.tw
  • Tel: +886-3-571-2121 ext. 56425
  • Fax: +886-3-572-4679
  • Address: Department of Applied Mathematics, National Chiao Tung University,1001 Ta Hsueh Road, Hsinchu, Taiwan 30050, ROC
Teaching
  • Fall Semester, 2024：

  • Spring Semester, 2024：
Vitae
  • Education
    • Ph.D. in Mathematics ,Heriot-Watt (1978)
    • M.S. in Mathematics, National Taiwan University (1974)
    • B.S. in Mathematics,National Taiwan University (1972)

  • Research Areas
    • Differential Equations
    • Dynamical System
    • Mathmetical Biology

  • Positions, Honors and Awards
      • Associate Professor, Department of Applied Mathematics National Chiao Tung University, 1978/ 08 - 1982/ 07
      • Professor, Department of Applied Mathematics National Chiao Tung University, 1982/ 08 --
      • Chairman of Department of Applied Math. 1982/02 - 1985/07
      • Dean of College of Science, 1996/ 08 - 2002/ 07
      • Distingushed award of National Science Council 1990-1992, 1992-1994, 1998-2000
      • SSChern award, ICCM 2001 Academic Award of Ministry of Education 2004
      • National Chair-Professor, Ministry of Education 2004-2007
      • University Chair-Professor, National Chiao-Tung University 2004-2010
      • Lifetime Chair-Professor, National Chiao-Tung University 2010-
      • National Chair-Professor, Ministry of Education 2013-2016
      • Lifetime National Chair -Professor, Ministry of Education.

  • Recent Research Projects
    • Multiplicative integer dynamical systems  104-2115-M-009-004-
    • Spatial entropy of multi-dimensional symbolic dynamical system 105-2115-M-009-001-  
    • On maximum meromorphic dynamic Zeta function 106-2115-M-009-004-
    • Classifications of maximum meromorphic dynamical Zeta functions 107-2115-M-009-006-

Selected Publications

    (A)   Refereed Papers：

    1. Song-Sun Lin & K. J. Brown, "Monotone techniques and semilinear elliptic boundary value problems", Proc. of the Royal Soc. of Edinburgh, 80A, 139-149, 1978.
    2. Song-Sun Lin & K. J. Brown, "Periodically perturbed conservative system and a global inverse function theorem", Nonlinear Analysis: Theory Methods and Applications, Vol. 4, 193-201, 1980.
    3. Song-Sun Lin & K. J. Brown, "On the existence of positive eigenfunctions for an eigenvalue problem with indefinite weight function", J. of Math. Anal. and Appl., Vol. 75, 112-120, 1980.
    4. Song-Sun Lin & K. J. Brown, "Bifurcation and stability results for an equation arising in population genetics", Annali Math. Pura ed Applicata, Vol. 128, 375-387, 1980.
    5. Song-Sun Lin, K. S. Cheng & S. B. Hsu, "Some results on global stability of a prodator-prey system", J. Math. Biol., Vol. 12, 115-126, 1981.
    6. Song-Sun Lin, "Monotone techniques and some existence-uniqueness theorems for two point boundary value problems", Proc. of the Royal Soc. of Edinburgh, 91A, 265-275, 1982.
    7. Song-Sun Lin, "Some results for semilinear differential equations at resonance", J. Math. Anal. Appl., Vol. 93, 572-592, 1983
    8. Song-Sun Lin, "Some uniqueness results for positive problems when a parameter is large", Chinese J. Math., Vol. 13, 67-81, 1985.
    9. Song-Sun Lin, "Symmetry Breaking for △u+2δeu=0 on disk with general boundary conditions", Processdings of the Symposium in Honor of Chen-Jung Hsu and Kung-Sing Shih, 27-29 June 1988, Natioal Taiwan University, Editors Ming-Chang Kang and Ko-Wei Lih, 137-173, 1988.
    10. Song-Sun Lin, K. J. Brown & A. Tertikas, "Existence and nonexistence of steady-state solutions for a selection-migratoin model in population genetics", J. Math. Bio., Vol. 27, 91-104, 1989.
    11. Song-Sun Lin, "On non-radially symmetric bifurcation in the annulus", J. Differential Equations, Vol. 80, 251-279, 1989.
    12. Song-Sun Lin, "On the existence of positive radial solutions for nonlinear elliptic equations in annular domains", J. Differential Equations, Vol. 81, 221-233, 1989.
    13. Song-Sun Lin, "Symmetry breaking for △u+2δe-u=0 on disk with general boundary conditions", Proc. of the Royal Soc. of Edinburgh, 113A, 105-117, 1989.
    14. Song-Sun Lin, "Positive radial solutions and non-radial bifurcation for semilinear elliptic equations in annular domains", J. Differential Equations, Vol. 86, 367-391, 1990.
    15. Song-Sun Lin & C. S. Lin, "Positive radial solutions for in and related topics", Applicable Analysis, Vol. 38, 121-160, 1990.
    16. Song-Sun Lin, "Symmetry breaking for semilinear elliptic equations on sectorial domains in R2", Proc. of the Royal Society of Edinburgh, 118A, 327-353, 1991.
    17. Song-Sun Lin, "On the number of positive solutions for nonlinear elliptic equations when a parameter is large", Nonlinear Analysis, TM&A, Vol. 16, 283-297, 1991.
    18. Song-Sun Lin and Feng-Ming Pai, "Existence and multiplicity of positive radial solutions for semilinear elliptic equations in annular domains", SIAM J. Math. Analysis, Vol. 22, 1500-1515, 1991.
    19. Song-Sun Lin, "Semilinear elliptic equations on singularly perturbed domains", Comm. in P. D. E., Vol. 16, 617-645, 1991.
    20. Song-Sun Lin and Min-gar Lee, Multiplicity of positive solutions for nonlinear elliptic equations on annulus, Chinese J. Math., Vol. 19, 257-276, 1991.
    21. Song-Sun Lin, "Existence of positive non-radial solutions for nonlinear elliptic equations in annular domains", Trans. A.M.S., Vol. 332, 775-791, 1992.
    22. Song-Sun Lin, "Existence of many positive nonradial solutions for nonlinear elliptic equations on annulus", J. Differential Equations, Vol. 103, 338-349, 1993.
    23. Song-Sun Lin, "Symmetry-breakings for semilinear elliptic equations on finite cylindrical domains, Proc. A.M.S., Vol. 117, 803-811, 1993.
    24. Song-Sun Lin and Min-gar Lee, "On the positive solutions for semilinear elliptic equations on annular domain with non-homogeneous Dirichlet boundary condition", J. Math. Anal. Appl., Vol. 181, 348-361, 1994.
    25. Song-Sun Lin, "Positive singular solutions for semilinear elliptic equation with supercritical growth", J. Differential Equations, Vol. 114, 57-76, 1994.
    26. Song-Sun Lin, "Asymptotic behavior of positive solutions to semilinear elliptic equations on expanding annuli", J. Differential Equations, Vol. 120, 255-228, 1995.
    27. Song-Sun Lin and Wen-Chi Kuan, "Numbers of equilibria for the equation of self-gravitating isentropic gas surrounding a solid ball", Japan J. of Industrial and Applied Mathematics, Vol. 13, 311-331, 1996.
    28. Song-Sun Lin, "Stability of gaseous stars in spherically symmetric motions", SIAM J. Math. Analysis, Vol. 28, 539-569, 1997.
    29. Song-Sun Lin and Cheng-Hsiung Hsu, "Some qualitative properties of the Riemann problem in gas dynamical combustion", J. Differential Equations, Vol. 140, 10-43, 1997.
    30. Song-Sun Lin and Chun-Chieh Fu, "On the critical mass of the collapse of gaseous star in spherically symmetric and isentropic motion", Japan J. of Industrial and Applied Mathematics, Vol. 15, 461-469, 1998.
    31. Song-Sun Lin and Chih-Wen Shih, "Complete stability for standard cellular neural networks", International J. of Bifurcation and Chaos, Vol. 9, 909-918, 1999.
    32. Song-Sun Lin, Cheng-Hsiung Hsu and Wenxian Shen, "Traveling waves in cellular neural networks", International J. of Bifurcation and Chaos, Vol. 9, 1307-1319, 1999.
    33. Song-Sun Lin and Jonq Juang, "Cellular Neural Networks: Mosaic pattern and spatial chaos", SIAM J. Appl. Math., Vol. 60, No. 3, 891-915, 2000.
    34. Song-Sun Lin and Cheng-Hsiung Hsu, "Traveling waves in lattice dynamical systems", J. Differential Equations, Vol. 164, 431-450, 2000.
    35. Song-Sun Lin, Cheng-Hsiung Hsu, Jonq Juang and Wen-Wei Lin, "Cellular neural networks: local patterns for general templates", International J. of Bifurcation and Chaos, Vol. 10, No. 7, 1645-1659, 2000.
    36. Song-Sun Lin and Tzi-Sheng Yang, "Spatial entropy of one dimensional cellular neural network", International J. of Bifurcation and Chaos, Vol. 10, No. 9, 2129-2140, 2000.
    37. Song-Sun Lin, Jonq Juang, Wen-Wei Lin and Shih-Feng Shieh, "Two dimensional spatial entropy", International J. of Bifurcation and Chaos, Vol. 10, No. 12, 2845-2852, 2000.
    38. Song-Sun Lin, Jung-Chso Ban and Chih-Wen Shih, "Number of stable equilibria in one dimensional cellular neural network", International J. of Bifurcation and Chaos, Vol. 11, No. 6, 1645-1653, 2001.
    39. Song-Sun Lin, Jung-Chao Ban, Kai-Ping Chien and Cheng-Hsiung Hsu, "Spatial disorder of CNN – with asymmetric out function", International J. of Bifurcation and Chaos, Vol. 11, No. 8, 2085-2095, 2001.
    40. Song-Sun Lin and Chun-Chieh Fu, "Uniqueness of positive radial solutions for semilinear elliptic equations on annular domains", Nonlinear Analysis, Vol. 44, 749-759, 2001.
    41. Song-Sun Lin, Cheng-Hsiung and T. Makino, "On the Relativistic Euler Equation", Methods and Applications of Analysis, Vol. 8, No. 1, 159-208, 2001.
    42. Song-Sun Lin and Cheng-Hsiung Hsu, "Spatial Disorder of Cellular Neural Networks", Japan Journal of Industrial and Applied Mathematics, Vol. 19, 143-161. (2002).
    43. Song-Sun Lin and Tzi-Sheng Yang, "On the spatial entropy and patterns of two-dimensional cellular neural networks", International J. of Bifurcation and Chaos, Vol. 12, 115-128. (2002).
    44. Song-Sun Lin, Jung-Chao Ban and Cheng-Hsiung Hsu, "Spatial disorder of Cellular Neural Network – with biased term", International J. of Bifurcation and Chaos, Vol. 12, No. 3, 525-534. (2002)
    45. Song-Sun Lin, Jung-Chao Ban and Cheng-Hsiung Hsu, "Devil's staircase of gap maps" International J. of Bifurcation and Chaos, Vol. 13, No. 1, 115-122. (2003).
    46. Song-Sun Lin, Cheng-Hsiung Hsu and Tetu Makino, "On spherically symmetric solution of the relativistic Euler equation" J. Differential Equations, Vol. 201, 1-24. (2004).
    47. Song-Sun Lin, Ting-Hui Yang and Wen-Wei Lin, "Bifarcations and chaos in two-cells cellular neural networks with periodic inputs", International J. of Bifurcation and Chaos, Vol. 14, No. 9, 3179-3204. (2004).
    48. Song-Sun Lin and Jung-Chao Ban, "The devil’s staircase dimensions and measure-theoretical entropy of maps with horizontal gap", Journal of Dynamics and Differential equations, Vol. 16, no. 3, 833-846. (2004).
    49. Song-Sun Lin and Jung-Chao Ban, “Patterns generation and transition matrices in multi-dimensional lattice models”, Discrete and Continuous Dynamical Systems, Vol. 13, 637-658. (2005).
    50. Song-Sun Lin, Cheng-Hsiung Hsu and Tetu Makino, “Smooth solutions to a class of quasilinear wave equations”, J. Differential Equations, 224, 229-257, (2006).
    51. Song-Sun Lin, Cheng-Hsiung Hsu and Tetu Makino, “Periodic solution to the 1-dimensional compressible Euler equation with gravity” Hyperbolic problems: Theory, Numerics and Application I, Tenth international conference in Osaka, Sept. 2004. Editor F. Asakura et al. 163-170, (2006), Yokohama Publishers, Inc. Yokohama, Japan.
    52. Song-Sun Lin, Jung-Chao Ban and Yin-Heng Lin, Patterns generation and spatial entropy in two-dimensional lattice models, Asian Journal of Mathematics, vol. 11, no. 3, 497-534. (2007).
    53. Song-Sun Lin, Jung-Chao Ban and Yin-Heng Lin, Three-dimensional Cellular Neural Networks and Patterns Generation Problems, International J. of Bifurcation and Chaos, vol. 18, No. 4, 957-984. (2008).
    54. Song-Sun Lin, Jung-Chao Ban, Chih-Hung Chang and Yin-Heng Lin, Spatial complexity in multi-layer cellular neural networks, J. Differential Equation, 246, 552-580 (2009).
    55. Song-Sun Lin and Wen-Guei Hu, Zeta functions for higher-dimensional shifts of finite type, International J. of Bifurcation and Chaos. Vol 19. No. 11, 3671-3689 (2009).
    56. Song-Sun Lin and Wen-Guei Hu, Nonemptiness problems of plane square tiling with two colors, Proceedings of American Mathematical Society 139 (2011) 1045-1059.
    57. Song-Sun Lin, Jung-Chao Ban and Chih-Hung Chang,"On the structure of multi-layer cellular neural networks", J. Differential Equation, 252, 4563-4597 (2012),
    58. Song-Sun Lin, Jung-Chao Ban, Wen-Guei Hu and Yin-Heng Lin, Zeta functions for two-dimensional shifts of finite type, Memoir.A.M.S.Vol. 221, No.1037(2013)
    59. Hung-Hsun Chen, Wen-Guei Hu, De-Jan Lai and Song-Sun Lin, “Nonemptiness problems of Wang tiles with three colors” , Theoretical Computer Science, Vol. 547 (2014) 34-45.
    60. Cheng-Hsiung Hsu, Song-Sun Lin and Chi-Ru Yang, “Smooth solutions of the one-dimensional compressible Euler equation with gravity”, J. Differential Equations 260, 708-732 (2016).
    61. Wen-Guei Hu and Song-Sun Lin, “On spatial entropy of multi-dimensional symbolic dynamical systems”, Discrete and Continuous Dynamical System, Vol. 36, 3705 - 3717 (2016)
    62. Jin-Yu Chen, Yu-Jie Chen, Wen-Guei Hu and Song-Sun Lin, “Spatial chaos of Wang tiles with two symbols”, J. Mathematical Physics, Vol. 57, 022704 (2016).
    63. Jung-Chao Ban, Wen-Guei Hu and Song-Sun Lin, “Pattern generation problems arising in multiplicative integer systems” accepted by Ergodic theory and Dynamic System, Vol.2017, 1-27. (2018)

    (B)   Conference Papers：

    1. Song-Sun Lin (1988), "On non-radially symmetric bifurcation in the annulus", Conf. on Solutions of nonlinear elliptic equations, July 12-15, RIMS, Kyoto, Japan.
    2. Song-Sun Lin (1989), "Positive radial solutions and non-radial bifurcation for semilinear elliptic equation in annular domains", Conf. on Nonlinear Differential Equations and Applications, Aug. 30-Sep. 2, RIMS, Kyoto, Japan.
    3. Song-Sun Lin (1990), "Existence of positive nonradial solutions for nonlinear elliptic equations in annular domains", International Congress of Math., Aug. 21-29, 1990, Kyoto, Japan.
    4. Song-Sun Lin (1990), "Semilinear elliptic equations on annular domains", Sino-Japanese Joint Seminar on Nonlinear PDE's with Emphasis on Reaction-Diffusion Aspects. Dec. 3-7, Taipei, Taiwan.
    5. Song-Sun Lin (1992), "Semilinear elliptic equations on annular domains", International Conference on nonlinear analysis, Aug. 30-Sep. 5, 1992, Xalapa, Veracruz, Mexico.
    6. Song-Sun Lin (1992), "Semilinear elliptic equations on annular domains", Deuxieme Rencontre Franco-Taiwanise D', E. D. P. nonlinear et Applications, Oct. 19-23, 1992, Paris, France.
    7. Song-Sun Lin (1994), "Singular solutions for supercritical equations", The Second Japan-Sino Joint Conference on Nonlinear Partial Differential Equations (I), Jan. 10-14, 1994, Kyoto, Japan.
    8. Song-Sun Lin (1994), "Semilinear equation on varying symmetric domains", The Second Japan-Sino Joint Conference on Nonlinear Partial Differential Equations (II), July 25-29, 1994, Ryukoku University, Seta, Ohtsu, Japan.
    9. Song-Sun Lin (1995), "Numbers and stability of equilibria of self-gravitating isentropic gas", Symposium on Mathematical Problems related to Fluid Flows, Theory and Numbers, March 25-28, 1995, Si-Tou, Nantou, Taiwan.
    10. Song-Sun Lin (1996), "Stability of gaseous stars", Sixth International Conference on Hyperbolic Problem, June 15-19, 1996, Hong-Kong.
    11. Song-Sun Lin (1996), "Cellular Neural Networks:Pattern formations and spatial chaos", Workshop on Differential Equations and Nonlinear Analysis, Oct. 28-Nov. 1, 1996, August de Lindoia, SP. Brail.
    12. Song-Sun Lin (1997), "Cellular Neural Networks: mosaic pattern and spatial chaos", Conference on Analysis and Applications March 30-April 5, 1997, Brisbane, Australia.
    13. Song-Sun Lin and Cheng-Hsiung Hsu (1998), "Patterns and waves in discrete dynamical systems", May 25-29, 1998, Parma, Italy.
    14. Song-Sun Lin (1998), "Cellular Neural Networks: Pattern and Waves", International Congress of Chinese Mathematicians (ICCM), December 12-16, 1998, Beijing.
    15. Song-Sun Lin (1999), "Cellular Neural Networks: Patterns and Waves", Equadiff 99 Conference, Aug 1-7, 1999, Berlin
    16. 2000 SIAM Conference on Dynamical System, Maui, Aug 9-13, 2000.
    17. Song-Sun Lin (2001), "Cellular Neural Networks: Patterns and Waves", The Second Pacific Rim Conference on Mathematics, Jan. 4-8, 2001, Taipei.
    18. Song-Sun Lin (2001), "Patterns generation in multi-dimensional lattice model", The second International Congress of Chinese Mathematicians, (ICCM 2001), Dec. 17-22, 2001, Taipei.
    19. Song-Sun Lin (2002), "Patterns generation and transition matrices in multi-dimensional lattice model". The 5-th Americans Conference on Differential Equations and Nonlinear Dynamics, July 7-12, 2002, Edmonton.
    20. Song-Sun Lin (2002), "Patterns generation and transition matrices in multi-dimensional lattice model". ICM 2002 Satellite Conference, New Directions in Dynamical Systems, Aug. 5-15, 2002, Kyoto.
    21. Song-Sun Lin (2003), “Patterns Generation and Transition Matrices in Higher Dimensional Lattice Models”, The 5th Sino-Philippine Symposium in Analysis, Quezon city, Philippine, Oct 23, 2003
    22. Song-Sun Lin (2003),“Bifurcations and chaos in Cellular Neural Networks”, International Workshop on Nonlinear Analysis and Kinetic Theory, Academia Sinica, Taipei, Dec 13-17 2003.
    23. Song-Sun Lin (2004), “Patterns Generation and Transition Matrices in Higher Dimensional Lattice Models”, The Workshop on Differential Equation and Mathematical Analysis, Jan 9-11, 2004, NTHU, HsinChu, Taiwan.
    24. ICCM 2004, Hong-Kong, Dec. 12-22, 2004, “Patterns generation and spatial entropy in multi-dimensional lattice models”.
    25. Japan-Taiwan Conference on Dynamical System, March 21-25, 2005, CTS, Hsinchu, Taiwan. (organizer).
    26. International Conference on Chaos and Dynamical Complexity, May 16-20, 2005, CTS, Hsinchu, Taiwan. (organizer).
    27. International Conference on Chaos and Dynamical Complexity, May 24-30, 2006, CTS, Hsinchu, Taiwan. (organizer).
    28. Song-Sun Lin, Jung-Chao Ban, Chih-Hung Chang and Wen-Guei Hu, “Complexity of two dimensional multi-layer cellular Neural Networks”. ICMCS, April 7-9, 2011, Quarzazate, Mocrocco.

    (C)   Others：

    1. Song-Sun Lin and Wen-Guei Hu,”The natural measure of symbolic dynamical system”,submitted(2013). (arXiv:1308.2996)
    2. Song-Sun Lin,Jung-Chao Ban,Wen-Guei Hu and Yin-Heng Lin,"Verification of mixing properties in two-dimensional shifts of finite type",submitted(2014). (arXiv:1112.2471)

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