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CURRICULUM VITAE
Saber N. Elaydi
ADDRESS: 
Trinity University 
CONTACT: 
Work: 
(210) 9998246 

Department of Mathematics 

Home: 
(210) 8250065 

One Trinity Place 

Email: 
selaydi@trinity.edu 

San Antonio, Texas 782127200 

Fax: 
(210) 9998264 
EDUCATION:
 Ph.D. in Mathematics, University of Missouri, Columbia, 1978.
 B.SC in Mathematics and Physics, AinShams University, 1965.
EMPLOYMENT:
 Chair, Trinity University, 2008
 Visiting Professor, Howard University, 20052006.
 Visiting Scholar: University of CaliforniaBerkeley (Spring 2001),
University of Augsburg, (Summer 2001), Birzeit University (Fall 2000),
University of Florence (Fall 1994).
 Professor, Trinity University, 1991present.
 Chair, Trinity University, 19911999.
 Associate Professor, Trinity University, 19891991. Associate
Professor, University of Colorado at Colorado Springs, 19841989.
Visiting Assistant Professor, Case Western Reserve University,
19831984. Assistant Professor, Kuwait University, 19781983.
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:
 CoEditorinChief, Journal of Biological Dynamics (JBD),
Taylor & Francis, 2006
 CoEditorinChief, 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 PacificAsian 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
 ViceChairman, The European Committee for establishing a
center of excellence in Mathematics and Theoretical Physics at
Birzeit University, (ECCEBirzeit), 2005
 VicePresident, Iternational Society of Education (ISE),
2006
PhD Students:
 Ziyad AlSharawi, 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, SpringerVerlag, 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 (EnglishArabicEnglish), 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, 20082013 (with Kelly Lyons).
 NSF Grant #0729519, 20072008 (With Jia Li, Shandelle Henson,
and Nicholas Ercolani)
 NSF Grant #0609974, 20062008.
 REUNSF grants, DMS9619837, 19972000, 20012004.
 Fulbright Grant, 2000.
 NSF Grant, DMS9706954, Asymptotic theory of difference equations,
19972000.
 PEW Foundation Grant, Chaos for undergraduates, 1995.
 NSF Grants, Int9805576, 19981999, 20002001.
 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):

Poplution Models with Allee effects, J. Biological Dynamics, Accepted
(with R. Sacker)

An Economic Model with Allee effect, J. Diff. Eq. Appl., Accepted.(with
R. Luis and H. Oliveria).

Stability and asymptoticity of Volterra Difference Equations: A progress
report, Journal of Computational and Applied Mathimatics.

Existence and stability of periodic orbits of periodic difference
equations with delays, International Journal of bifurcation and chaos, 18
(2008) 115 (with Angelos and AlSharawi)

On the stochastic BevertonHolt equation with survival rates, J. Diff. Eq.
Appl., Vol. 14 (2008), 175190 (with Bezandry and Diagana)

On the asymptotic stability of linear Volterra difference equations of
convolution type, J. Diff. Eq. Appl., Vol.13(12), (2007), 10791084 (with
Messina and Vecchio)

Population Models in almost periodic environmen, J. Diff. Eq. Appl., Vol.
13(4), (2007), 239260 (with Diagana, Yakubu).

Periodic difference equations, population biology and the CushingHenson
conjecture, Mathematical Biosciences 201 (2006), 195207 (with Sacker).

Skewproduct dynamical systems: Applications to difference equations, Proceedings of the UAE Math Day (with Sacker).

An extension of Sharkovsky's theorem to periodic difference equations, J. Math. Anal. Appl. (with Alsharawi, Angelos, Rakesh).

Periodic difference equations, population biology and the CushingHenson conjectures (with Sacker).

Global Stability of periodic orbits of nonautonomous difference equations in population biology and the CushingHenson conjectures (with Sacker).

Global stability of periodic orbits of nonautonomous difference equations and population biology, Journal of Differential Equations, Vol. 208, pp. 258273 (2005) (with Sacker).

Difference Equations versus Differential Equations, a possible equivalence, Physica D, Vol. 195/ 12 (2004), pp. 2949 (with Letellier et al).

Basin of attraction of periodic orbits and population biology, J. Diff. Eq. Appl., Vol. 10(10), 881888 (2004), (with Sacker).

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, 349358 (with Aulbach, Ziegler).

Asymptotic stability of linear difference equations of advanced type, J. Computational Anal. Appl., Vol. 6, No. 2, 423428 (2004) (with Dannan).

Nonautonomous difference equations: Open problems and conjectures, Proceedings of the 8th international conference on difference equations, The Fields Institute, 423428 (2004).

Difference equations from discretization of continuous epidemic models with disease in the prey, Canadian Applied Math Quarterly, Vol. 11, pp. 93101, 2003(with Jang).

Stability of hyperbolic and nonhyperbolic fixed points of onedimensional maps, J. Diff. Eq. and Appl. 9(2003), 449457(with Dannan, Ponomarenko).

Is the world evolving discretely? , Advances in Applied Math, 31(2003), 19.

Poincarétype solutions of systems of difference equations, J. Math. Anal. Appl. 275 (2002), 6983 (with AbuSaris, Jang).

Stability theory of Volterra difference equations, Advances in Stability Theory at the End of the 20th Century, (ed. Martynyuk), Taylor & Francis, 2002, pp. 124155 (with Dannan, Li).

Ztransform, Encyclopedia of Mathematics, (ed. Hazewinkel), Kluwer, 2002, pp. 448449.

Global stability of cycles: LotkaVolterra competition model with stocking, J. Diff. Eq. and Appl. 8 (2002), 537549 (with Yakubu).

Basin of attraction of stable cycles, J. Diff. Eq. and Appl. 8 (2002), 755760 (with Yakubu).

Asymptotics for linear difference equations II: Applications, New Trends in Difference Equations, Taylor & Francis, London, 2002, pp. 111133.

Discrete competitive and cooperative models of LotkaVolterra type, J. Computational and Applied Analysis 3 (2001), 5373 (with P. Liu).

The Discrete Analogue of the Putzer Algorithm, Linear Algebra Gems, MAA Notes, (ed. D. Carlson et al.), 2001, pp. 249253.

Nonstandard discretization methods for some biological models, a chapter in "Applications of nonstandard finite difference schemes," edited by R. Mickens, World Scientific Publishers, 2000.

Periodic solutions of difference equations, J. Diff. Eq. and Appl. 6 (2000), 203232 (with Dannan, Liu).

Extension of chaos to general topological spaces, Panamer. Math. J. 10 (2000), 6171 (with Awartani).

On some open problems in difference equations. Proceedings of the Second Palestinian International Conference on Mathematics, pp. 89114,World Scientific Publications, 2000.

Asymptotic for linear difference equations I: Basic Theory, J. Diff. Eq. and Appl. 5 (1999), 563589.

Difference equations in combinatorics, number theory, and orthogonal polynomials, J. Diff. Eq. and Appl. 5 (1999), 379392.

Asymptotic equivalence for difference equations with infinite delay, J. Diff. Eq. and Appl. 5 (1999), 123.

Recent developments in the asymptotics of difference equations, New Developments in Difference Equations and Applications, Proceedings, Gordon and Breach, (1999), 161181.

Uniform asymptotic stability in linear Volterra difference equations, J. Diff. Eq. and Appl. 3 (1998), 203218 (with Murakami).

Dichotomy and trichotomy of difference equations, J. Diff. Eq. and Appl. 3 (1998), 417448 (with Janglajew).

On the Computation of A^{N}, SIAM Review 40 (1998), 965971.

Stability of integrodifferential systems of nonconvolution type, Mathematical Inequalities and Applications 1 (1998), 423430.

New trends in the asymptotics of difference equations, Proceedings of the Third International Conference on Difference Equations, Taipei, Gordon and Breach, 1999, 161181.

Asymptotic theory for noninvertible systems, Gordon & Breach, 1997, 155164 (with Papaschinopolos, Schinas).

Asymptotic stability versus exponential stability in linear Volterra difference equations of convolution type, J. Diff. Eq. and Appl. 2 (1996), 401410 (With Murakami).

Global stability of nonlinear delay difference equations, J. Diff. Eq. and Appl. 2 (1996), 8796 (with Kocic, Li).

On a Converse of Sharkovsky's Theorem, American Math. Monthly 103 (May 1996), 386392.

An extension of Levinson's Theorem to asymptotically Jordan difference equations, J. Diff. Eq. and Appl. 1 (1995), 369390.

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, 175183 (with Zhang).

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, 163174 (with Zhang).

Asymptotic theory for delay difference equations, J. Diff. Eq. and Appl. 1 (1995), 99116 (with Gyori).

Global stability of nonlinear Volterra difference systems, J. Differential Equations and Dynamical Systems 2 (1994), 337345 (with Kocic).

Stability and periodicity of difference equations with finite delay, Funkcialaj Ekvacioj 37 (1994), 401413 (with Zhang).

Periodicity and stability of linear Volterra Difference Systems, J. Math Anal. and Appl. 181 (1994), 483492.

Global stability of difference equations, Proceedings of the First World Congress of Nonlinear Analysis '92, Walter de Gruyter Publisher (1996), 11311138 (Ed. V. Lakshmikantham).

Stability of Volterra difference equations of convolution type, in "Dynamical Systems" (ed. Liao ShanTao et al.), pp. 6673, World Scientific, 1993.

Weakly Anosov diffeomorphisms and exponential trichotomy, Libertas Mathematica 12 (1992), 99107 (with Farran).

Stability of integrodifferential systems of nonconvolution type, Proceedings International Symposium on Functional Differential Equations, Kyoto, World Scientific (1991), 6774.

On variation of equicontinuity in dynamical systems, Bulletin Australian Math. Soc. 42 (1991), 391397 (with Farran).

Asymptotic stability of linear systems with infinite delay, (Ed. Yoshizawa and Kato), World Scientific (1991), 6774.

The existence of periodic solutions of Volterra equations with infinite delay, Differential Equations, Stability and Control, (ed.Elaydi), Marcel Dekker, Inc., (1990), 105113 (with Cushman).

Recent results on stability of differential, integrodifferential equations and dynamical systems, Proceedings International Conference on Nonlinear Analysis and Applications to Biomathematics, (ed. Murty), 6079, Eskay Enterprises (Printing Division), Pradesh, India, (1990).

Strongly stable semidynamical systems with global backward extensions, Applicable Analysis 39 (1990), 113 (with Farran).

Exponential dichotomy and trichotomy of nonlinear differential equations, Diff. and Integral Eq. 3 (1990), 12011334 (with Hacek).

Stability of difference equations via Liapunov functions, Proceedings of the International Conference on Differential Equations, (ed.Aftabizadeh), 235238, Ohio University Press, (1989) (with Peterson).

A unified approach to stability problems in integrodifferential equations, J. Math. Anal. and Appl. 143 (1989), 503531 (with Sivasundaram).

Asymptotic stability in general dynamical systems, Nonlinear Analysis, Theory, Methods & Appl. 13 (1989), 657669 (with Kaul).

Lipschitz stability of nonlinear systems of differential equations II: Liapunov functions, J. Math. Anal. Appl. 143 (1989), 517529 (with Dannan).

Nearly periodic dynamical systems, Appl. Analysis 27 (1988), 243251 (with Ahmad).

Semiflows with global extensions II: notions of negative stability, Nonlinear Analysis, Theory, Methods & Appl. 12 (1988), 733746 (with Kaul).

Lipschitz stability of nonlinear integrodifferential equations, J. Applied Math. And Comp. 27 (1988), (with Rao).

Exponential trichotomy of differential systems, J. Math. Analysis and Appl. 129 (1988), 362374 (with Hajek).

Some remarks on nonlinear dichotomy and trichotomy, Nonlinear Analysis and Appl. (ed. Lakshmikantham), 175178, Marcel Dekker, Inc., (1987) (with Hajek).

Exponentially asymptotically stable systems, Appl. Analysis 25 (1987), 243252 (with Farran).

Stability of limit and prolongation sets in semiflows, Appl. Analysis 23 (1987), 261276 (with Kaul).

Semiflows with global extensions, Nonlinear Analysis, Theory, Methods & Appl. 10 (1986), 713726 (with Kaul).

Lipschitz stability of nonlinear systems of differential equations, J. Math. Analysis & Appl. 113 (1986), 562577 (with Dannan).

A flow associated with a semiflow, Trends in Theory and Practice on Nonlinear Analysis, Arlington, Texas, North Holland, (1985), 155159 (with Kaul).

Exponential dichotomy of nonlinear systems of differential equations, Trends in Theory and Practice on Nonlinear Analysis, Arlington, Texas, North Holland, (1985), 145153 (with Hajek).

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 MissouriRolla, (1985), 4153 (ed.Henderson).

Lipschitz stable dynamical systems, Nonlinear Analysis, Theory, Methods & Appl. 9 (1985), 729738 (with Farran).

On weak isometrics and their embeddings in flows, Nonlinear Analysis, Theory, Methods & Appl. 8 (1984), 14371441 (with Farran).

Isometrics and certain dynamical systems, Bull. Austral. Math. Soc. 30 (1984), 239248 (with Farran).

Semidynamical systems with nonunique global backward extensions II: the negative aspects, Funkcialaj. Ekvacioj 27 (1984), 85100.

Attraction in topolgical dynamics, J. Differential Eq. 51 (1984), 116125.

Transformation groups of strong characteristic O, Bulletin Austral. Math. Soc. 27 (1983), 243248.

Semidynamical systems with nonunique global backward extensions, Funkcialaj. Ekvacioj 26 (1983), 173187.

On some stability notions in topological dynamics, J. Differential Eq. 47 (1983), 2334.

On characteristic O and locally weakly almost periodic flows, Math. Japonica 27 (1982) 613624.

Flows of almost strong characteristic O with generative phase groups, Nonlinear Analysis, Theory, Methods & Appl. 6 (1982) (with Kaul).

Pequicontinuous flows, Funkcialaj Ekvacioj (1982), 4349.

Precursion and transformation groups of characteristic O, J. Univ. Kuwait 9 (1982), 807815.

Criteria for regionally recurrent flows, Proc. Amer. Math. Soc. 85 (1982), 461468.

On locally weakly almost periodic transformation groups, Bull. Austral. Math. Soc. 25 (1982), 215219.

Strongly stable dynamical systems, Proceedings of the International Conference on Functional Differential Systems and Related Topics, Blazejewko, Poland,(ed.M.. Kiselewicz), Zielona Gora, (1981), 105110.

Weakly equicontinuous flows, Funkcialaj. Ekvacioj 24 (1981), 317324.

On equicontinuous transformation groups, Bull. Austral. Math. Soc. 24 (1981), 367372.

Active preferred sets in almost regular flows, Math. Japonica 26 (1981), 367372.

A note on the number of normal subgroups of a group, J. Univ Kuwait 8 (1981), 95106.

A theorem on almost periodicity, J. Univ. Kuwait (Science) 6 (1979), 3133.

Preferred sets in topological dynamics, Proc. Amer. Math. Soc. 63 (1977), 334338 (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)
