Books and Most Recent Journal Articles

• The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, 1994 (with Paul Waltman).
• Monotone Dynamical Systems, an Introduction to the Theory of Competitive and Cooperative Systems, American Mathematical Society, Mathematical Surveys and Monographs 1995.

• A model of microbial growth in a plug flow reactor with wall attachment, with M. Ballyk, Mathematical Biosciences 158, 5-126,1999.
• Asymptotically autonomous semiflows: chain recurrence and Liapunov functions, with K. Mischaikow & H.Thieme, Trans. AMS 347, 1995, 1669-1685 pdf
  
• Microbial Competition for nutrient and wall sites in plug flow, with D.Jones, SIAM J.Appl.Math. 60,1576-1600,2000.
• Global asymptotic stability of traveling waves in delayed reaction-diffusion equations, with X.-Q. Zhao, SIAM J. Math. Anal., 31, 514-534.
• Chain transitivity, attractivity and strong repellors for semidynamical systems,  with X.-Q. Zhao and M.W. Hirsch, J.Dynamics and Diff. Eqns.13, 2001. 
• Robust Persistence for semi-dynamical systems, with X.-Q.
  Zhao, Proc. WCNA 2000, Nonlinear Analysis 47 , 2001, 6169-6179. pdf
  
• Competitive exclusion in a discrete-time size-structured chemostat model, with X.-Q. Zhao., Discrete and Contin. Dynamical Systems 1,2001, 183-191.
• Stable coexistence and bi-stability for competitive systems on ordered Banach spaces, with H. Thieme, J. Diff. Eqns. 176, 2001, 195-212.
• Microbial competition in reactors with wall attachment: a comparison of chemostat and plug flow models, with M. Ballyk and D. Jones, Microbial Ecology, 41, 2001.
• Bacterial wall attachment in a flow reactor, with D. Jones,H.Kojouharov,D. Le, SIAM J. Appl. Math. 62, 2002, 1728-1771.
• Bacterial wall attachment in a flow reactor: mixed culture, with D. Jones,H.Kojouharov,D.Le, Canadian Applied Math. Quart., to appear.
• Strong positivity of solutions to parabolic and elliptic equations on nonsmooth domains, with D.Le , 275, 2002, 208-221.
• Feedback control for the chemostat, with P. de Leenheer,  J. Math. Biol. 46 (2003) 1, 48-70.
• Competition for essential resources: a brief review, with B. Li, Fields Institute Communications,36, 2003, 213-227.
• Virus Dynamics: a global analysis, with P. De Leenheer,  SIAM J. Appl. Math.63, 1313-1327,  2003.
• Monotone systems, a mini-review, with M.W. Hirsch, in Positive Systems. Proceedings of the First Multidisciplinary Symposium on Positive Systems (POSTA 2003). Luca Benvenuti, Alberto De Santis and Lorenzo Farina (Eds.) Lecture Notes on Control and Information Sciences vol. 294, Springer Verlag, Heidelberg, 2003.
• Traveling waves in a bio-reactor model, with X.-Q. Zhao, Nonlinear Analysis: Real World Applications 5 (2004) 895-909.
• Planar competitive and cooperative difference equations, J. Difference Eqns. & Appl. 3, 1998, 335-357.
• The Poincare-Bendixson Theorem for monotone cyclic feedback systems, with J.Mallet-Paret, J. Dynamics & Diff. Eqns.2,1990, 367-421.
• Monotone Maps: A Review, J. Difference Eqns.& Appl. 11(2005) 379-398.
• Competition in the Chemostat: Some remarks, with P. de Leenheer & B. Li, Canadian Applied Math Quarterly, 11, Fall 2003.
• Monotone Dynamical Systems, with M. Hirsch, Handbook of Differential Equations, Ordinary Differential Equations (second volume), eds. A.Canada,P.Drabek,A.Fonda, Elsevier, 239-357,2005.
• Asymptotically Stable Equilibria for Monotone Semiflows, with M. Hirsch, Discrete and Continuous Dynamical Systems 14,
  385-398, 2006. (erata pdf )
• Generic Quasiconvergence for strongly order preserving semiflows: a new approach, with M. Hirsch,J. Dynamics and
  Diff. Eqns. 16 (2004) 433-440.
• Non-monotone systems decomposable into monotone systems with negative feedback, with G. Enciso and E. Sontag, Journal of Differential Equations, Volume 224, Issue 1, 1 May 2006, Pages 205-227
• The discrete dynamics of monotonically decomposable maps, J. Math. Biol. 53, 2006, 747-758.pdf
• Biofilms and the Plasmid Maintenance question, with Mudassar Imran and Don Jones,  Mathematical Biosciences,
  193, issue 2, 2005, p183-204. pdf
• Multiple limit cycles in the standard model of three species competition for three essential resources, with B. Li and S.
  Baer,  J. Math. Biol. 52, 2006, 745-760. pdf
• A resource-based model of microbial quiescence, with T. Malik, J. Math. Biology 53, 2006, 231-252. pdf
• The pharmacodynamics of antibiotic treatment, with M.Imran, Journal of Computational and Mathematical Methods
  in Medicine 7, 2006, 229 - 263. pdf
• The Dynamics of Bacterial Infection, Innate Immune Response, and Antibiotic Treatment , with M. Imran,
  Discrete \& Cont. Dynamical Systems, ser. B. 8, 2007, 127-143. pdf
• Quasiconvergence and stability for strongly order preserving semiflows,
         with H. Thieme, SIAM J. Math. Anal., 21, 1990, 673-692. pdf
• Convergence for strongly order preserving semiflows, with H.Thieme,
         SIAM J. Math. Anal., 22, 1991, 1081-1102.  pdf
• Abstract functional differential equations and reaction-diffusion
         systems, with R. Martin, Trans. of A.M.S., 321, 1990, 1-44. pdf
• Reaction-Diffusion Systems with Time Delays:Monotonicity Invariance,
         Comparison and Convergence, with R.Martin, J. reine und
         angewandte Mathematik, 413, 1991, 1-35.  pdf
•  Prevalent behavior of strongly order preserving semiflows,
  with G. Enciso, M.W. Hirsch, J.Dynamics and Diff. Eqns. 20, Number 1 / March, 2008, p115  pdf
• Dynamics of Stoichiometric Bacteria-Algae interactions in the epilimnion, H. Wang, Y. Kuang, J. Elser,  SIAM J. Applied Math. 68, p. 503 (2007) pdf
• Global dynamics of microbial competition for two resources with internal storage, B. Li, J. Math. Biol. 55 (2007)
  481-515. pdf
• Global stability for mixed-monotone systems, J. Difference Eqns. & Appl., 14 Issue 10, October 2008.
  doi:10.1080/10236190802332126  pdf
• Does Dormancy increase Fitness of Bacterial Populations in Time-Varying Environments, T. Malik, Bulletin of Mathematical
  Biology, 70, Number 4 / May, p 1140, 2008 pdf
  
• Models of Virulent Phage Growth with application to Phage Therapy, SIAM J. Appl. Math. 68 (2008) 1717-1737.
  http://dx.doi.org.ezproxy1.lib.asu.edu/10.1137/070704514, pdf
• Persistence in a discrete-time stage structured fungal disease model, with P. Salceanu, J. Biol. Dynamics.  3, 2009 , 271 - 285,  pdf
  
• Persistence in a discrete-time stage-structured epidemic model, with P. Salceanu, J. Difference Eqns. & Appl. pdf
  
• Liapunov exponents and persistence in discrete dynamical systems, with P. Salceanu, Discrete & Cont. Dynam. Systems-B pdf
• Liapunov exponents and uniform weak normally repelling invariant sets, with P. Salceanu, conf. proc. POSTA09, to appear, Lect. Notes in Control and Information Sciences, Springer. pdf
  

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