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Bourama Toni

Toni, Dr. Bourama, PhD

Mathematics & Economics

Professor of Mathematics

Phone: 804-524-5486
Location: Hunter McDaniel 202Sd


Ph.D. in Mathematics. [Differential Analysis and Dynamical Systems] Université de Montréal, Canada
Computer Algebra Systems: Mathematica-Maple-G.A.P.-Macaulay-Auto-Matlab-SAGE
Mathematics Education: Didactique des Mathématiques: Ecole Normale Supérieure, Paris, France
Mathematical Methods in Biology, Medicine and Pharmacology: University of British Columbia and Université de Montréal, Canada

Research & Creative Interests:


           Pure Mathematics

  • Differential Analysis & Dynamical Systems (Critical Periods-Limit Cycles-Isochronous Systems)
  • Almost Periodicity (Almost, Pseudo-almost and almost Automorphic Solutions in Banach/Hilbert Spaces; Quasi-Limit Cycles)
  • P-Adic Dynamics (P-Adic Limit Cycles- P-Adic Almost Periodicity in Non-Archimedean and Berkovich Spaces)

          Applied Mathematics:

  • Limit Cycles Oscillations in Engineering, Physics and Biosciences
  • P-Adic Matrix Computation: P-Adic Parallel Linear Systems (Banded matrices)
  • Feedback Loops Analysis: Signed Matrices Dynamics
  • Game Theory: Cooperative/Non-Cooperative Models. Nash Limit Cycles

           Mathematics and the Arts:

  • Acrylic Paintings [mathematical Perspectives and “Impossible” P-Adic Worlds]. Prose-Poetry

Professional Experience

  • Summer 2015: Visiting Researcher at Naval Undersea Warfare Center (NUWC), Newport, RI

  • Full Professor of Mathematics, Virginia State University:

  • Adjunct Faculty, Virginia Commonwealth University

  • Visiting Professor at the Center for Research in Mathematics (CRM), Canada

  • Associate Professor at Lane College, Tennessee

  • Professor-Investigador tenured at Universidad Autonoma del Estado de Morelos (UAEM), Cuernavaca, Mexico

  • Senior Lecturer at the Walter Sisulu University (WSU), Eastern Cape South Africa

  • Assistant Professor at Dalhousie University, NS, Canada


           Fall 2015

  • Calculus III
  • Difference Equations (Graduate)
  • Abstract Algebra (Graduate)

           Spring 2015

  • Advanced Calculus I
  • Basic Mathematics
  • Difference Equations (Graduate)
  • Real Analysis (Graduate)

Selected VSU Publications/Scholarly Work  

  • Book: Interdisciplinary Mathematical Research and Applications. Springer PROMS. To appear Spring 2016
  • Book Chapter: Dynamical Roles of Jacobian Feedback Loops and Qualitative Modeling: in Springer PROMS 90, 205-240 (2014)
  • Book: New Frontiers of Multidisciplinary Research in STEAM-H. Springer PROMS Vol. 90 2014  
  • Book Chapter: Almost and Pseudo-almost Limit Cycles with Applications to Quasi-periodic waves. In Springer PROMS 37, 233-265(2012) (with M. Watts)
  • Planar Pseudo-almost Limit Cycles and Applications to Solitary Waves. Cubo: A Mathematical Journal. Vol.15(01), 131-149. (2013)
  • Book: Advances in Interdisciplinary Mathematical ResearchSpringer Proceedings in Mathematics &Statistics, Vol. 37. (2013) ISBN: 978-1-4614-6344-3 
  • Book Chapter: Almost and Pseudo-almost Limit Cycles with applications to quasi-periodic waves. Book Chapter. Springer Proceedings in Mathematics and Statistics. Vol. 37. 233-277 (2013) pp 233-265 (with M. Watts)
  • Book: Bridging Mathematics, Statistics, Engineering and TechnologySpringer Proceedings in Mathematics & Statistics. Vol. 24 (2012) ISBN 13: 9781461445586
  • A mathematical function to evaluate surgical complexity of cleft lip and palate. Computer Methods and Programs in Biomedicine. Vol. 94 Issue 3, pp 232-238. (2009) (with M. Posadas, L. Vega)
  • Jacobian Feedback Loops II: Stability and Instability. International Journal of Evolution Equations. Vol. 2(4) (2008). 355-366. 
  • Existence and Uniqueness of pseudo almost periodic solutions to some classes of semilinear differential equations and applications. Nonlinear Analysis. Series A: Theory, Methods & Applications.64 (2006) 2442-2453. (with T. Diagana and G. N’Guérékata). 
  • Upper Bounds for Limit Cycles from Isochronous Period Annulus via birational Linearization. Discrete and Continuous Dynamical Systems. Suppl.Vol.( 2005) pp 846-853.
  • Jacobian Feedback Loop Analysis I. International Journal of Evolution Equations. Vol 1(4) (2005). 415-428
  • A similarity Function to evaluate the orthodontic condition in patients with cleft lip and palate. Medical Hypotheses, vol. 63(1)(2004), 35-41. (with L. Vega and M. Posadas). 
  • Mathematical analysis of a Pharmacodynamic model without plasma concentrations to extend its applicability. Medical Hypotheses, 2003 60(3):453-457. (with A. Ocampo-Nava). 

Selected Non-VSU Papers

  • Higher order Branching of Periodic orbits from Polynomial Isochrones. Elect.J.Diff.Eqns, 35, 1-15(1999)
  • Bifurcation of Critical Periods: Cubic vector fields in Kapteyn’s normal form. Quaestiones Mathematicae, 22(1), 43-61 (1999)
  • Feedback Loops for Chaotic Dynamics with an application to Lorenz system. Fields Institute Communications Series and American Mathematical Society (AMS), 21, 473-484(1999) (with D. Thieffry, R. Bulajich)
  • The dynamics of a two dimensional model for Electrochemical corrosion using Feedback Circuit and Nullcline analysis. The Journal of Physical Chemistry B., 102(21), 4118-4122(91998) (with P. Parmananda, R. Bulajich and D. Thieffry)
  • Local Bifurcations of Critical Periods in the reduced Kukles systems. Can.J.Math. 48(2), 338-358 (1997) (with C. Rousseau)
  • Linearization of Isochronous Centers. Journal of Differential Equations, 121, 67-108 (1995) (with P. Mardesic, C. Rousseau)

Most Recent Presentations

  • NAVSEA Division Newport Lecture Series. July 2015
  • College of William & Mary, Math Seminar. April 2015
  • Old Dominion University Math Colloquium. March 2015
  • University of Virginia Mathematical Physics seminar. February 201
  • Virginia Commonwealth University (VCU), Analysis and Logic seminar. February 2015
  • Howard University. Mathematical Seminary. November 201

Creative Work: Painting and Prose-Poetry

Solo Exhibition: “A Mathematical Mind in the Arts” October 14-November 30. Meredith Art Gallery, and Press Release by The Progress-Index Petersburg, VA

Sample Artwork:           


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