San Antonio, Texas

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CURRICULUM VITAE

Saber N. Elaydi

ADDRESS: Trinity University CONTACT: Work: (210) 999-8246
Department of Mathematics Home: (210) 825-0065
One Trinity Place E-mail: selaydi@trinity.edu
San Antonio, Texas 78212-7200 Fax: (210) 999-8264

EDUCATION:

  • Ph.D. in Mathematics, University of Missouri, Columbia, 1978.
  • B.SC in Mathematics and Physics, Ain-Shams University, 1965.

EMPLOYMENT:

  • Chair, Trinity University, 2008-
  • Visiting Professor, Howard University, 2005-2006.
  • Visiting Scholar: University of California-Berkeley (Spring 2001), University of Augsburg, (Summer 2001), Birzeit University (Fall 2000), University of Florence (Fall 1994).
  • Professor, Trinity University, 1991-present.
  • Chair, Trinity University, 1991-1999.
  • Associate Professor, Trinity University, 1989-1991. Associate Professor, University of Colorado at Colorado Springs, 1984-1989. Visiting Assistant Professor, Case Western Reserve University, 1983-1984. Assistant Professor, Kuwait University, 1978-1983.

RESEARCH INTERESTS:

  • Difference Equations/Discrete Dynamical Systems and Mathematical Biology.

HONORS:

  • Instructor of the Year Award, College of Engineering and Applied Sciences, University of Colorado, 1988.
  • Fulbright Scholar, Fall 2000.

ACADEMIC ACTIVITIES:

  • Co-Editor-in-Chief, Journal of Biological Dynamics (JBD), Taylor & Francis, 2006-
  • Co-Editor-in-Chief, Journal of Difference Equations and Applications(JDEA), Taylor & Francis, 1994-
  • Member of the editorial board of the International Journal of Difference Equations, 2006-
  • Member of the editorial board of Journal of Computational and Applied Analysis, 1998-
  • Member of the editorial board of the International Journal of Mathematics and Computer Science, 2005-
  • Member of the editorial board of CUBO, A Mathematical Journal, 1999-
  • Member of the editorial board of Pacific-Asian Journal of Mathematics, 2005-
  • Editor: Book series "Advances in Discrete Mathematics and Applications", Taylor & Francis, 1995-

PROFESSIONAL ACTIVITIES:

  • President, International Society of Difference Equations (ISDE), 2005-
  • Director, European Advanced Studies, 2006-
  • Vice-Chairman, The European Committee for establishing a center of excellence in Mathematics and Theoretical Physics at Birzeit University, (ECCE-Birzeit), 2005-
  • Vice-President, Iternational Society of Education (ISE), 2006-

PhD Students:

  • Ziyad Al-Sharawi, University of Central Michigan, PhD, May 2006.
  • Rafael Llius, Technical University of Lisbon

PUBLICATIONS:

Books:

  • Discrete Chaos: Applications in Science and Engineering, Second Edition, Chapman & Hall/CRC London, 2008.
  • An Introduction to Difference Equations, Springer-Verlag, New York, Third Edition, 2005.
  • (Editor) Difference equations, Special functions and Orthogonal Polynomials, World Scientific, 2007.
  • (Editor) Mathematics Research at the leading edge, NOVA 2006.
  • (Editor) Difference Equations and Discrete Dtnamical Systems, Proceedings of the 9th International Conference, University of Southern California, World Scientific, 2005
  • (Editor) Difference and Differential Equations, Fields Institute Communications, American Mathematical Society, Providence, 2004.
  • (Editor) New Progress in Difference Equations, Chapman & Hall\CRC, Boca Raton, 2004.
  • (Editor) New Trends in Difference Equations, Taylor & Francis, London, 2002.
  • (Editor) Mathematics & Mathematics Education, World Scientific, Singapore, 2002.
  • (Editor) Proceedings of Mathematics Conference, World Scientific, Singapore, 2000.
  • (Editor) New Developments in Difference Equations and Applications, Gordon and Breach, 1999.
  • (Editor) Advances in Difference Equations, Gordon and Breach, 1997.
  • (Editor) Difference Equations and Applications, Gordon and Breach, 1995.
  • (Editor) Differential Equations; Stability and Control, Marcel Dekker, Inc., New York, 1990.
  • Dictionary of Mathematics (English-Arabic-English), Kuwait Foundation for the Advancement of Science, 1984, (with Dannan et al.) Math. Reviews, 86j:00015 (1986), P. 4396.
  • Encyclopedia of Mathematics, Vol. I, II, III and IV, (in Arabic), Kuwait Foundation for the Advancement of Science, 1984, (with Dannan et al.), Math Reviews, 86j:00015, P. 4396.

Recent Grants:

  • USDA Grant, 2008-2013 (with Kelly Lyons).
  • NSF Grant #0729519, 2007-2008 (With Jia Li, Shandelle Henson, and Nicholas Ercolani)
  • NSF Grant #0609974, 2006-2008.
  • REU-NSF grants, DMS-9619837, 1997-2000, 2001-2004.
  • Fulbright Grant, 2000.
  • NSF Grant, DMS-9706954, Asymptotic theory of difference equations, 1997-2000.
  • PEW Foundation Grant, Chaos for undergraduates, 1995.
  • NSF Grants, Int-9805576, 1998-1999, 2000-2001.
  • University of Le Havre summer Grant, France, Summer 2002.
  • Trinity University Faculty Development Grants, Summer 1990, 1995, 2003.
  • The University of Augsburg Grant, Summer 2001.

Books in progress:

  • Discrete Mathematical Models in Life Sciences (with David Ribble)

Papers published or accepted for publication (in refereed journals):

  1. Poplution Models with Allee effects, J. Biological Dynamics, Accepted (with R. Sacker)
  2. An Economic Model with Allee effect, J. Diff. Eq. Appl., Accepted.(with R. Luis and H. Oliveria).
  3. Stability and asymptoticity of Volterra Difference Equations: A progress report, Journal of Computational and Applied Mathimatics.
  4. Existence and stability of periodic orbits of periodic difference equations with delays, International Journal of bifurcation and chaos, 18 (2008) 1-15 (with Angelos and Al-Sharawi)
  5. On the stochastic Beverton-Holt equation with survival rates, J. Diff. Eq. Appl., Vol. 14 (2008), 175-190 (with Bezandry and Diagana)
  6. On the asymptotic stability of linear Volterra difference equations of convolution type, J. Diff. Eq. Appl., Vol.13(12), (2007), 1079-1084 (with Messina and Vecchio)
  7. Population Models in almost periodic environmen, J. Diff. Eq. Appl., Vol. 13(4), (2007), 239-260 (with Diagana, Yakubu).
  8. Periodic difference equations, population biology and the Cushing-Henson conjecture, Mathematical Biosciences 201 (2006), 195-207 (with Sacker).
  9. Skew-product dynamical systems: Applications to difference equations, Proceedings of the UAE Math Day (with Sacker).
  10. An extension of Sharkovsky's theorem to periodic difference equations, J. Math. Anal. Appl. (with Alsharawi, Angelos, Rakesh).
  11. Periodic difference equations, population biology and the Cushing-Henson conjectures (with Sacker).
  12. Global Stability of periodic orbits of nonautonomous difference equations in population biology and the Cushing-Henson conjectures (with Sacker).
  13. Global stability of periodic orbits of nonautonomous difference equations and population biology, Journal of Differential Equations, Vol. 208, pp. 258-273 (2005) (with Sacker).
  14. Difference Equations versus Differential Equations, a possible equivalence, Physica D, Vol. 195/ 1-2 (2004), pp. 29-49 (with Letellier et al).
  15. Basin of attraction of periodic orbits and population biology, J. Diff. Eq. Appl., Vol. 10(10), 881-888 (2004), (with Sacker).
  16. Asymptotic solutions of a discrete Schrodinger equation arising from a Dirac equation with random mass, New Progress of Difference Equations, (Ed. Aulbach, Elaydi, Ladas), Chapman & Hall/CRC, 2004, 349-358 (with Aulbach, Ziegler).
  17. Asymptotic stability of linear difference equations of advanced type, J. Computational Anal. Appl., Vol. 6, No. 2, 423-428 (2004) (with Dannan).
  18. Nonautonomous difference equations: Open problems and conjectures, Proceedings of the 8th international conference on difference equations, The Fields Institute, 423-428 (2004).
  19. Difference equations from discretization of continuous epidemic models with disease in the prey, Canadian Applied Math Quarterly, Vol. 11, pp. 93-101, 2003(with Jang).
  20. Stability of hyperbolic and non-hyperbolic fixed points of one-dimensional maps, J. Diff. Eq. and Appl. 9(2003), 449-457(with Dannan, Ponomarenko).
  21. Is the world evolving discretely? , Advances in Applied Math, 31(2003), 1-9.
  22. Poincaré-type solutions of systems of difference equations, J. Math. Anal. Appl. 275 (2002), 69-83 (with Abu-Saris, Jang).
  23. Stability theory of Volterra difference equations, Advances in Stability Theory at the End of the 20th Century, (ed. Martynyuk), Taylor & Francis, 2002, pp. 124-155 (with Dannan, Li).
  24. Z-transform, Encyclopedia of Mathematics, (ed. Hazewinkel), Kluwer, 2002, pp. 448-449.
  25. Global stability of cycles: Lotka-Volterra competition model with stocking, J. Diff. Eq. and Appl. 8 (2002), 537-549 (with Yakubu).
  26. Basin of attraction of stable cycles, J. Diff. Eq. and Appl. 8 (2002), 755-760 (with Yakubu).
  27. Asymptotics for linear difference equations II: Applications, New Trends in Difference Equations, Taylor & Francis, London, 2002, pp. 111-133.
  28. Discrete competitive and cooperative models of Lotka-Volterra type, J. Computational and Applied Analysis 3 (2001), 53-73 (with P. Liu).
  29. The Discrete Analogue of the Putzer Algorithm, Linear Algebra Gems, MAA Notes, (ed. D. Carlson et al.), 2001, pp. 249-253.
  30. Nonstandard discretization methods for some biological models, a chapter in "Applications of nonstandard finite difference schemes," edited by R. Mickens, World Scientific Publishers, 2000.
  31. Periodic solutions of difference equations, J. Diff. Eq. and Appl. 6 (2000), 203-232 (with Dannan, Liu).
  32. Extension of chaos to general topological spaces, Panamer. Math. J. 10 (2000), 61-71 (with Awartani).
  33. On some open problems in difference equations. Proceedings of the Second Palestinian International Conference on Mathematics, pp. 89-114,World Scientific Publications, 2000.
  34. Asymptotic for linear difference equations I: Basic Theory, J. Diff. Eq. and Appl. 5 (1999), 563-589.
  35. Difference equations in combinatorics, number theory, and orthogonal polynomials, J. Diff. Eq. and Appl. 5 (1999), 379-392.
  36. Asymptotic equivalence for difference equations with infinite delay, J. Diff. Eq. and Appl. 5 (1999), 1-23.
  37. Recent developments in the asymptotics of difference equations, New Developments in Difference Equations and Applications, Proceedings, Gordon and Breach, (1999), 161-181.
  38. Uniform asymptotic stability in linear Volterra difference equations, J. Diff. Eq. and Appl. 3 (1998), 203-218 (with Murakami).
  39. Dichotomy and trichotomy of difference equations, J. Diff. Eq. and Appl. 3 (1998), 417-448 (with Janglajew).
  40. On the Computation of AN, SIAM Review 40 (1998), 965-971.
  41. Stability of integrodifferential systems of nonconvolution type, Mathematical Inequalities and Applications 1 (1998), 423-430.
  42. New trends in the asymptotics of difference equations, Proceedings of the Third International Conference on Difference Equations, Taipei, Gordon and Breach, 1999, 161-181.
  43. Asymptotic theory for noninvertible systems, Gordon & Breach, 1997, 155-164 (with Papaschinopolos, Schinas).
  44. Asymptotic stability versus exponential stability in linear Volterra difference equations of convolution type, J. Diff. Eq. and Appl. 2 (1996), 401-410 (With Murakami).
  45. Global stability of nonlinear delay difference equations, J. Diff. Eq. and Appl. 2 (1996), 87-96 (with Kocic, Li).
  46. On a Converse of Sharkovsky's Theorem, American Math. Monthly 103 (May 1996), 386-392.
  47. An extension of Levinson's Theorem to asymptotically Jordan difference equations, J. Diff. Eq. and Appl. 1 (1995), 369-390.
  48. Periodic solutions of Volterra difference equations with infinite delay II: the nonlinear case, in "Proceedings of the first International Conference on Difference Equations" (Ed. S. Elaydi et al.), Gordon and Breach, 1995, 175-183 (with Zhang).
  49. Periodic solutions of Volterra difference equations with infinite delay I: the linear case, in "Proceedings of the first International Conference on Difference Equations" (Ed. S. Elaydi), Gordon and Breach, 1995, 163-174 (with Zhang).
  50. Asymptotic theory for delay difference equations, J. Diff. Eq. and Appl. 1 (1995), 99-116 (with Gyori).
  51. Global stability of nonlinear Volterra difference systems, J. Differential Equations and Dynamical Systems 2 (1994), 337-345 (with Kocic).
  52. Stability and periodicity of difference equations with finite delay, Funkcialaj Ekvacioj 37 (1994), 401-413 (with Zhang).
  53. Periodicity and stability of linear Volterra Difference Systems, J. Math Anal. and Appl. 181 (1994), 483-492.
  54. Global stability of difference equations, Proceedings of the First World Congress of Nonlinear Analysis '92, Walter de Gruyter Publisher (1996), 1131-1138 (Ed. V. Lakshmikantham).
  55. Stability of Volterra difference equations of convolution type, in "Dynamical Systems" (ed. Liao Shan-Tao et al.), pp. 66-73, World Scientific, 1993.
  56. Weakly Anosov diffeomorphisms and exponential trichotomy, Libertas Mathematica 12 (1992), 99-107 (with Farran).
  57. Stability of integrodifferential systems of nonconvolution type, Proceedings International Symposium on Functional Differential Equations, Kyoto, World Scientific (1991), 67-74.
  58. On variation of equicontinuity in dynamical systems, Bulletin Australian Math. Soc. 42 (1991), 391-397 (with Farran).
  59. Asymptotic stability of linear systems with infinite delay, (Ed. Yoshizawa and Kato), World Scientific (1991), 67-74.
  60. The existence of periodic solutions of Volterra equations with infinite delay, Differential Equations, Stability and Control, (ed.-Elaydi), Marcel Dekker, Inc., (1990), 105-113 (with Cushman).
  61. Recent results on stability of differential, integrodifferential equations and dynamical systems, Proceedings International Conference on Nonlinear Analysis and Applications to Biomathematics, (ed. Murty), 60-79, Eskay Enterprises (Printing Division), Pradesh, India, (1990).
  62. Strongly stable semidynamical systems with global backward extensions, Applicable Analysis 39 (1990), 1-13 (with Farran).
  63. Exponential dichotomy and trichotomy of nonlinear differential equations, Diff. and Integral Eq. 3 (1990), 1201-1334 (with Hacek).
  64. Stability of difference equations via Liapunov functions, Proceedings of the International Conference on Differential Equations, (ed.-Aftabizadeh), 235-238, Ohio University Press, (1989) (with Peterson).
  65. A unified approach to stability problems in integrodifferential equations, J. Math. Anal. and Appl. 143 (1989), 503-531 (with Sivasundaram).
  66. Asymptotic stability in general dynamical systems, Nonlinear Analysis, Theory, Methods & Appl. 13 (1989), 657-669 (with Kaul).
  67. Lipschitz stability of nonlinear systems of differential equations II: Liapunov functions, J. Math. Anal. Appl. 143 (1989), 517-529 (with Dannan).
  68. Nearly periodic dynamical systems, Appl. Analysis 27 (1988), 243-251 (with Ahmad).
  69. Semiflows with global extensions II: notions of negative stability, Nonlinear Analysis, Theory, Methods & Appl. 12 (1988), 733-746 (with Kaul).
  70. Lipschitz stability of nonlinear integrodifferential equations, J. Applied Math. And Comp. 27 (1988), (with Rao).
  71. Exponential trichotomy of differential systems, J. Math. Analysis and Appl. 129 (1988), 362-374 (with Hajek).
  72. Some remarks on nonlinear dichotomy and trichotomy, Nonlinear Analysis and Appl. (ed. Lakshmikantham), 175-178, Marcel Dekker, Inc., (1987) (with Hajek).
  73. Exponentially asymptotically stable systems, Appl. Analysis 25 (1987), 243-252 (with Farran).
  74. Stability of limit and prolongation sets in semiflows, Appl. Analysis 23 (1987), 261-276 (with Kaul).
  75. Semiflows with global extensions, Nonlinear Analysis, Theory, Methods & Appl. 10 (1986), 713-726 (with Kaul).
  76. Lipschitz stability of nonlinear systems of differential equations, J. Math. Analysis & Appl. 113 (1986), 562-577 (with Dannan).
  77. A flow associated with a semiflow, Trends in Theory and Practice on Non-linear Analysis, Arlington, Texas, North Holland, (1985), 155-159 (with Kaul).
  78. Exponential dichotomy of nonlinear systems of differential equations, Trends in Theory and Practice on Nonlinear Analysis, Arlington, Texas, North Holland, (1985), 145-153 (with Hajek).
  79. Some notions of stability in differential equations and dynamical systems, Proceedings of Midwest Conference on Differential Equations, Iowa City, IA, October 1983. Institute of Applied Math., University of Missouri-Rolla, (1985), 41-53 (ed.-Henderson).
  80. Lipschitz stable dynamical systems, Nonlinear Analysis, Theory, Methods & Appl. 9 (1985), 729-738 (with Farran).
  81. On weak isometrics and their embeddings in flows, Nonlinear Analysis, Theory, Methods & Appl. 8 (1984), 1437-1441 (with Farran).
  82. Isometrics and certain dynamical systems, Bull. Austral. Math. Soc. 30 (1984), 239-248 (with Farran).
  83. Semidynamical systems with nonunique global backward extensions II: the negative aspects, Funkcialaj. Ekvacioj 27 (1984), 85-100.
  84. Attraction in topolgical dynamics, J. Differential Eq. 51 (1984), 116-125.
  85. Transformation groups of strong characteristic O, Bulletin Austral. Math. Soc. 27 (1983), 243-248.
  86. Semidynamical systems with nonunique global backward extensions, Funkcialaj. Ekvacioj 26 (1983), 173-187.
  87. On some stability notions in topological dynamics, J. Differential Eq. 47 (1983), 23-34.
  88. On characteristic O and locally weakly almost periodic flows, Math. Japonica 27 (1982) 613-624.
  89. Flows of almost strong characteristic O with generative phase groups, Nonlinear Analysis, Theory, Methods & Appl. 6 (1982) (with Kaul).
  90. P-equicontinuous flows, Funkcialaj Ekvacioj (1982), 43-49.
  91. P-recursion and transformation groups of characteristic O, J. Univ. Kuwait 9 (1982), 807-815.
  92. Criteria for regionally recurrent flows, Proc. Amer. Math. Soc. 85 (1982), 461-468.
  93. On locally weakly almost periodic transformation groups, Bull. Austral. Math. Soc. 25 (1982), 215-219.
  94. Strongly stable dynamical systems, Proceedings of the International Conference on Functional Differential Systems and Related Topics, Blazejewko, Poland,(ed.-M.. Kiselewicz), Zielona Gora, (1981), 105-110.
  95. Weakly equicontinuous flows, Funkcialaj. Ekvacioj 24 (1981), 317-324.
  96. On equicontinuous transformation groups, Bull. Austral. Math. Soc. 24 (1981), 367-372.
  97. Active preferred sets in almost regular flows, Math. Japonica 26 (1981), 367-372.
  98. A note on the number of normal subgroups of a group, J. Univ Kuwait 8 (1981), 95-106.
  99. A theorem on almost periodicity, J. Univ. Kuwait (Science) 6 (1979), 31-33.
  100. Preferred sets in topological dynamics, Proc. Amer. Math. Soc. 63 (1977), 334-338 (with Lam).

Papers in Progress

  • On the connectedness of global attractos, Preprint (with Miller)
  • Population Models with Allee effect: A new Model (with Sacker)
  • An Economic model with Allee effect (with Luis and Oliveria)

Questions and comments concerning this page are to be addressed to selaydi@trinity.edu .