De Leenheer, Patrick

• 2765652
  Angeli, David(4-LNDIC-EL); De Leenheer, Patrick(1-FL); Sontag, Eduardo D.(1-RTG)
  Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws. (English summary)
  SIAM J. Appl. Math. 71 (2011), no. 1, 128–146.
  92C40 (34C11 37C75 92C42)
  
• 2765652
  Angeli, David(4-LNDIC-EL); De Leenheer, Patrick(1-FL); Sontag, Eduardo D.(1-RTG)
  Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws. (English summary)
  SIAM J. Appl. Math. 71 (2011), no. 1, 128–146.
  92C40 (34C11 37C75 92C42)
  
• 2672536
  Angeli, David(I-FRNZ-I); De Leenheer, Patrick(1-FL); Sontag, Eduardo(1-RTG)
  Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates. (English summary)
  J. Math. Biol. 61 (2010), no. 4, 581–616.
  92C42 (80A30 92C40)
  
• 2672532
  De Leenheer, Patrick(1-FL); Dockery, Jack(1-MTS); Gedeon, Tomáš(1-MTS); Pilyugin, Sergei S.(1-FL)
  Senescence and antibiotic resistance in an age-structured population model. (English summary)
  J. Math. Biol. 61 (2010), no. 4, 475–499.
  92D25 (34A33 34D05 92D15 93D05)
  
• 2649313
  Wang, Liming(1-CA3); De Leenheer, Patrick(1-FL); Sontag, Eduardo D.(1-RTG)
  Conditions for global stability of monotone tridiagonal systems with negative feedback. (English summary)
  Systems Control Lett. 59 (2010), no. 2, 130--138.
  93D20 (34A33 34D20)
  
• 2583205
  de Leenheer, Patrick(1-FL); Angeli, David(I-FRNZ-I); Sontag, Eduardo D.(1-RTG)
  Monotone chemical reaction networks [translation of MR2343862]. (Hungarian. English, Hungarian summary)
  Translated by Judit Várdai.
  Alkalmaz. Mat. Lapok 26 (2009), no. 2, 381--402.
  34C12 (34D05)
  
• 2529207
  De Leenheer, Patrick(1-FL); Cogan, N. G.(1-FLS)
  Failure of antibiotic treatment in microbial populations. (English summary)
  J. Math. Biol. 59 (2009), no. 4, 563--579.
  92D30 (92C40)
  
• 2469624
  De Leenheer, Patrick(1-FL)
  Within-host virus models with periodic antiviral therapy. (English summary)
  Bull. Math. Biol. 71 (2009), no. 1, 189--210.
  92C50
  
• 2467296
  Ackleh, Azmy S.(1-LA); De Leenheer, Patrick(1-FL)
  Discrete three-stage population model: persistence and global stability results. (English summary)
  J. Biol. Dyn. 2 (2008), no. 4, 415--427.
  92D25 (39A11)
  
• 2427521
  De Leenheer, Patrick(1-FL); Pilyugin, Sergei S.(1-FL)
  Immune response to a malaria infection: properties of a mathematical model. (English summary)
  J. Biol. Dyn. 2 (2008), no. 2, 102--120.
  92D30 (34C60 34D23)
  
• 2373385
  Keeran, Willard S.(1-FL); De Leenheer, Patrick(1-FL); Pilyugin, Sergei S.(1-FL)
  Feedback-mediated coexistence and oscillations in the chemostat. (English summary)
  Discrete Contin. Dyn. Syst. Ser. B 9 (2008), no. 2, 321--351.
  92D25 (37N25)
  
• 2352231
  Angeli, David(I-FRNZ-I); De Leenheer, Patrick(1-FL); Sontag, Eduardo(1-RTG)
  A Petri net approach to persistence analysis in chemical reaction networks. (English summary) Biology and control theory: current challenges, 181--216,
  Lecture Notes in Control and Inform. Sci., 357, Springer, Berlin, 2007.
  92E20 (34A34 68Q85)
  
• 2374484
  Angeli, David(I-FRNZ-I); De Leenheer, Patrick(1-FL); Sontag, Eduardo D.(1-RTG)
  A Petri net approach to the study of persistence in chemical reaction networks. (English summary)
  Math. Biosci. 210 (2007), no. 2, 598--618.
  92C40 (92D40 92E20)
  
• 2343862
  De Leenheer, Patrick(1-FL); Angeli, David(I-FRNZ-I); Sontag, Eduardo D.(1-RTG)
  Monotone chemical reaction networks. (English summary)
  J. Math. Chem. 41 (2007), no. 3, 295--314.
  92E20 (34C12)
  
• 2291872
  Keeran, Willard S.(1-FL); De Leenheer, Patrick(1-FL); Pilyugin, Sergei S.(1-FL)
  Circular and elliptic orbits in a feedback-mediated chemostat. (English summary)
  Discrete Contin. Dyn. Syst. Ser. B 7 (2007), no. 4, 779--792 (electronic).
  92D25 (34C25 92C37)
  
• 2293767
  Mazenc, Frédéric; Malisoff, Michael(1-LAS); De Leenheer, Patrick(1-FL)
  On the stability of periodic solutions in the perturbed chemostat. (English summary)
  Math. Biosci. Eng. 4 (2007), no. 2, 319--338 (electronic).
  92D25 (34C25 34D20)
  
• 2250245
  De Leenheer, Patrick(1-FL); Pilyugin, Sergei S.(1-FL)
  Feedback-mediated oscillatory coexistence in the chemostat. (English summary) Positive systems, 97--104,
  Lecture Notes in Control and Inform. Sci., 341, Springer, Berlin, 2006.
  92D25 (93B52)
  
• 2235513
  De Leenheer, Patrick(1-FL); Levin, Simon A.(1-PRIN); Sontag, Eduardo D.(1-RTG); Klausmeier, Christopher A.(1-GAIT)
  Global stability in a chemostat with multiple nutrients. (English summary)
  J. Math. Biol. 52 (2006), no. 4, 419--438.
  92D25 (34D23)
  
• 2217846
  De Leenheer, Patrick(1-FL); Angeli, David(I-FRNZ-I); Sontag, Eduardo D.(1-RTG)
  Crowding effects promote coexistence in the chemostat. (English. English summary)
  J. Math. Anal. Appl. 319 (2006), no. 1, 48--60.
  34C12 (34D23 92D25)
• 2201714
  Malisoff, Michael(1-LAS); De Leenheer, Patrick(1-FL)
  A small-gain theorem for monotone systems with multivalued input-state characteristics. (English. English summary)
  IEEE Trans. Automat. Control 51 (2006), no. 2, 287--292.
  93C10 (93D25)
• 2130751
  De Leenheer, Patrick(1-FL); Angeli, David(I-FRNZ-I); Sontag, Eduardo D.(1-RTG)
  On predator-prey systems and small-gain theorems. (English. English summary)
  Math. Biosci. Eng. 2 (2005), no. 1, 25--42.
  34C12 (34D20 92D25 92D40 93D15)
• 2074383 (2005b:93140)
  Angeli, D.(I-FRNZ-I); De Leenheer, P.(1-RTG-CS); Sontag, E. D.(1-RTG)
  A small-gain theorem for almost global convergence of monotone systems. (English. English summary)
  Systems Control Lett. 52 (2004), no. 5, 407--414.
  93D20 (93C10)
• 2132198
  de Leenheer, Patrick(1-FL); Li, Bingtuan(1-LSVL); Smith, Hal L.(1-AZS-MS)
  Competition in the chemostat: some remarks.
  Can. Appl. Math. Q. 11 (2003), no. 3, 229--248.
  92D25 (34C60 92D40)
• 2019317 (2004i:92026)
  De Leenheer, Patrick(1-AZS-MS); Angeli, David(I-FRNZ-I); Sontag, Eduardo D.(1-RTG)
  Small-gain theorems for predator-prey systems. (English. English summary)
  Positive systems (Rome, 2003), 191--198,
  Lecture Notes in Control and Inform. Sci., 294,
  Springer, Berlin, 2003.
  92D25 (34D20)
• 2019314 (2004i:92025)
  de Leenheer, Patrick(1-AZS-MS); Angeli, David(I-FRNZ-I); Sontag, Eduardo D.(1-RTG)
  A feedback perspective for chemostat models with crowding effects. (English. English summary)
  Positive systems (Rome, 2003), 167--174,
  Lecture Notes in Control and Inform. Sci., 294,
  Springer, Berlin, 2003.
  92D25 (34D23)
• 1989905 (2004b:34136)
  De Leenheer, Patrick(1-AZS-MS); Smith, Hal L.(1-AZS-MS)
  Virus dynamics: a global analysis. (English. English summary)
  SIAM J. Appl. Math. 63 (2003), no. 4, 1313--1327 (electronic).
  34D23 (34A34)
• 1957009 (2004a:93034)
  De Leenheer, Patrick(1-AZS); Smith, Hal(1-AZS)
  Feedback control for chemostat models. (English. English summary)
  J. Math. Biol. 46 (2003), no. 1, 48--70.
  93B52 (34C60 49N90 92D25)
• 2134037
  De Leenheer, Patrick(1-AZS); Aeyels, Dirk(B-GHNT-SY)
  Stabilization of positive systems with first integrals. (English. English summary)
  Automatica J. IFAC 38 (2002), no. 9, 1583--1589.
  93D15
• 1920271 (2003g:34076)
  Aeyels, Dirk(B-GHNT-SY); De Leenheer, Patrick(1-AZS-MS)
  Extension of the Perron-Frobenius theorem to homogeneous systems. (English. English summary)
  SIAM J. Control Optim. 41 (2002), no. 2, 563--582 (electronic).
  34C12 (34D05 34D23 37C65 93D20)
• 2021961 (2004f:93104)
  De Leenheer, Patrick(B-GHNT-SY); Aeyels, Dirk(B-GHNT-SY)
  Stabilization of positive linear systems. (English. English summary)
  Systems Control Lett. 44 (2001), no. 4, 259--271.
  93D15
• 1878229 (2002i:93058)
  De Leenheer, Patrick(1-AZS); Aeyels, Dirk(B-GHNT-SY)
  Stability properties of equilibria of classes of cooperative systems. (English. English summary)
  IEEE Trans. Automat. Control 46 (2001), no. 12, 1996--2001.
  93D10 (93C10)