메뉴 건너뛰기




Volumn 6244 LNCS, Issue , 2010, Pages 267-279

Parametric qualitative analysis of ordinary differential equations: Computer algebra methods for excluding oscillations (extended abstract) (invited talk)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMIC METHODS; ANDRONOV-HOPF BIFURCATION; COMPUTER ALGEBRA METHODS; EXTENDED ABSTRACTS; FIXED POINTS; HARD PROBLEMS; HILBERT'S 16TH PROBLEM; INVITED TALK; LIMIT CYCLE; POLYNOMIAL SYSTEMS; QUALITATIVE ANALYSIS; SCIENCE AND ENGINEERING; STABLE LIMIT CYCLE;

EID: 78049383594     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-15274-0_24     Document Type: Conference Paper
Times cited : (6)

References (41)
  • 1
    • 0035997405 scopus 로고    scopus 로고
    • Centennial history of Hilbert's 16th Problem
    • Ilyashenko, Y.: Centennial history of Hilbert's 16th Problem. Bull. Am. Math. Soc., New Ser. 39(3), 301-354 (2002)
    • (2002) Bull. Am. Math. Soc., New Ser. , vol.39 , Issue.3 , pp. 301-354
    • Ilyashenko, Y.1
  • 3
    • 49449117050 scopus 로고    scopus 로고
    • Algebraic approaches to stability analysis of biological systems
    • Niu, W., Wang, D.: Algebraic approaches to stability analysis of biological systems. Mathematics in Computer Science 1(3), 507-539 (2008)
    • (2008) Mathematics in Computer Science , vol.1 , Issue.3 , pp. 507-539
    • Niu, W.1    Wang, D.2
  • 4
    • 52949127380 scopus 로고    scopus 로고
    • Investigating generic methods to solve Hopf bifurcation problems in algebraic biology
    • Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. eds., Springer, Heidelberg
    • Sturm, T., Weber, A.: Investigating generic methods to solve Hopf bifurcation problems in algebraic biology. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds.) AB 2008. LNCS, vol. 5147, pp. 200-215. Springer, Heidelberg (2008)
    • (2008) AB 2008. LNCS , vol.5147 , pp. 200-215
    • Sturm, T.1    Weber, A.2
  • 5
    • 38149139488 scopus 로고    scopus 로고
    • On proving the absence of oscillations in models of genetic circuits
    • Anai, H., Horimoto, K., Kutsia, T. eds., Springer, Heidelberg
    • Boulier, F., Lefranc, M., Lemaire, F., Morant, P., Ürgüplü , A.: On proving the absence of oscillations in models of genetic circuits. In: Anai, H., Horimoto, K., Kutsia, T. (eds.) Ab 2007. LNCS, vol. 4545, pp. 66-80. Springer, Heidelberg (2007)
    • (2007) Ab 2007. LNCS , vol.4545 , pp. 66-80
    • Boulier, F.1    Lefranc, M.2    Lemaire, F.3    Morant, P.4    Ürgüplü, A.5
  • 6
    • 52949124116 scopus 로고    scopus 로고
    • Applying a rigorous quasisteady state approximation method for proving the absence of oscillations in models of genetic circuits
    • Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. eds., Springer, Heidelberg
    • Boulier, F., Lefranc, M., Lemaire, F., Morant, P. E.: Applying a rigorous quasisteady state approximation method for proving the absence of oscillations in models of genetic circuits. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds.) AB 2008. LNCS, vol. 5147, pp. 56-64. Springer, Heidelberg (2008)
    • (2008) AB 2008. LNCS , vol.5147 , pp. 56-64
    • Boulier, F.1    Lefranc, M.2    Lemaire, F.3    Morant, P.E.4
  • 7
    • 1142307783 scopus 로고    scopus 로고
    • Symbolic equilibrium point analysis in parameterized polynomial vector fields
    • Ganzha, V. G., Mayr, E. W., Vorozhtsov, E. V. eds., Yalta, Ukraine, September
    • El Kahoui, M., Weber, A.: Symbolic equilibrium point analysis in parameterized polynomial vector fields. In: Ganzha, V. G., Mayr, E. W., Vorozhtsov, E. V. (eds.) Computer Algebra in Scientific Computing (CASC 2002), Yalta, Ukraine, pp. 71-83 (September 2002)
    • (2002) Computer Algebra in Scientific Computing (CASC 2002) , pp. 71-83
    • El Kahoui, M.1    Weber, A.2
  • 8
    • 0345851264 scopus 로고    scopus 로고
    • Deciding Hopf bifurcations by quantifier elimination in a software-component architecture
    • El Kahoui, M., Weber, A.: Deciding Hopf bifurcations by quantifier elimination in a software-component architecture. Journal of Symbolic Computation 30(2), 161-179 (2000)
    • (2000) Journal of Symbolic Computation , vol.30 , Issue.2 , pp. 161-179
    • El Kahoui, M.1    Weber, A.2
  • 10
    • 27744465496 scopus 로고    scopus 로고
    • Toric ideals and graph theory to analyze hopf bifurcations in mass action systems
    • Gatermann, K., Eiswirth, M., Sensse, A.: Toric ideals and graph theory to analyze hopf bifurcations in mass action systems. Journal of Symbolic Computation 40(6), 1361-1382 (2005)
    • (2005) Journal of Symbolic Computation , vol.40 , Issue.6 , pp. 1361-1382
    • Gatermann, K.1    Eiswirth, M.2    Sensse, A.3
  • 11
    • 0001787356 scopus 로고
    • Sur les curbes définiés par des équations différentielles
    • Bendixson, I.: Sur les curbes définiés par des équations différentielles. Acta Math. 24, 1-88 (1901)
    • (1901) Acta Math. , vol.24 , pp. 1-88
    • Bendixson, I.1
  • 12
    • 0003285244 scopus 로고
    • Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
    • Springer, Heidelberg
    • Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences, vol. 42. Springer, Heidelberg (1983)
    • (1983) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 14
    • 0002355108 scopus 로고
    • The complexity of linear problems in fields
    • Weispfenning, V.: The complexity of linear problems in fields. Journal of Symbolic Computation 5 (1 & 2), 3-27 (1988)
    • (1988) Journal of Symbolic Computation , vol.5 , Issue.1-2 , pp. 3-27
    • Weispfenning, V.1
  • 15
    • 80052987943 scopus 로고
    • Real quantifier elimination is doubly exponential
    • Davenport, J. H., Heintz, J.: Real quantifier elimination is doubly exponential. Journal of Symbolic Computation 5 (1-2), 29-35 (1988)
    • (1988) Journal of Symbolic Computation , vol.5 , Issue.1-2 , pp. 29-35
    • Davenport, J.H.1    Heintz, J.2
  • 16
    • 0006762975 scopus 로고    scopus 로고
    • Solving systems of strict polynomial inequalities
    • Strzebonski, A.: Solving systems of strict polynomial inequalities. Journal of Symbolic Computation 29(3), 471-480 (2000)
    • (2000) Journal of Symbolic Computation , vol.29 , Issue.3 , pp. 471-480
    • Strzebonski, A.1
  • 17
    • 33746869360 scopus 로고    scopus 로고
    • Cylindrical algebraic decomposition using validated numerics
    • Strzebonski, A. W.: Cylindrical algebraic decomposition using validated numerics. J. Symb. Comput. 41(9), 1021-1038 (2006)
    • (2006) J. Symb. Comput. , vol.41 , Issue.9 , pp. 1021-1038
    • Strzebonski, A.W.1
  • 18
    • 33744926650 scopus 로고    scopus 로고
    • QEPCAD B: A system for computing with semi-algebraic sets via cylindrical algebraic decomposition
    • Brown, C. W.: QEPCAD B: A system for computing with semi-algebraic sets via cylindrical algebraic decomposition. ACM SIGSAM Bulletin 38(1), 23-24 (2004)
    • (2004) ACM SIGSAM Bulletin , vol.38 , Issue.1 , pp. 23-24
    • Brown, C.W.1
  • 19
    • 0002443040 scopus 로고    scopus 로고
    • REDLOG: Computer algebra meets computer logic
    • Dolzmann, A., Sturm, T.: REDLOG: Computer algebra meets computer logic. ACM SIGSAM Bulletin 31(2), 2-9 (1997)
    • (1997) ACM SIGSAM Bulletin , vol.31 , Issue.2 , pp. 2-9
    • Dolzmann, A.1    Sturm, T.2
  • 20
    • 52949098720 scopus 로고    scopus 로고
    • Redlog online resources for applied quantifier elimination
    • Sturm, T.: Redlog online resources for applied quantifier elimination. Acta Academiae Aboensis, Ser. B 67(2), 177-191 (2007)
    • (2007) Acta Academiae Aboensis, Ser. B. , vol.67 , Issue.2 , pp. 177-191
    • Sturm, T.1
  • 22
    • 0031212059 scopus 로고    scopus 로고
    • Simplification of quantifier-free formulae over ordered fields
    • Dolzmann, A., Sturm, T.: Simplification of quantifier-free formulae over ordered fields. Journal of Symbolic Computation 24(2), 209-231 (1997)
    • (1997) Journal of Symbolic Computation , vol.24 , Issue.2 , pp. 209-231
    • Dolzmann, A.1    Sturm, T.2
  • 24
    • 35048836354 scopus 로고    scopus 로고
    • Diploma thesis, Universität Passau, D-94030 Passau, Germany September
    • Gilch, L. A.: Effiziente Hermitesche Quantorenelimination. Diploma thesis, Universität Passau, D-94030 Passau, Germany (September 2003)
    • (2003) Effiziente Hermitesche Quantorenelimination
    • Gilch, L.A.1
  • 25
    • 33845229628 scopus 로고    scopus 로고
    • Generic Hermitian quantifier elimination
    • Buchberger, B., Campbell, J. eds., Springer, Heidelberg
    • Dolzmann, A., Gilch, L. A.: Generic Hermitian quantifier elimination. In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 80-93. Springer, Heidelberg (2004)
    • (2004) AISC 2004. LNCS (LNAI) , vol.3249 , pp. 80-93
    • Dolzmann, A.1    Gilch, L.A.2
  • 26
    • 33845230582 scopus 로고    scopus 로고
    • New domains for applied quantifier elimination
    • Ganzha, V. G., Mayr, E. W., Vorozhtsov, E. V. eds., Springer, Heidelberg
    • Sturm, T.: New domains for applied quantifier elimination. In: Ganzha, V. G., Mayr, E. W., Vorozhtsov, E. V. (eds.) CASC 2006. LNCS, vol. 4194, pp. 295-301. Springer, Heidelberg (2006)
    • (2006) CASC 2006. LNCS , vol.4194 , pp. 295-301
    • Sturm, T.1
  • 27
    • 36448945078 scopus 로고    scopus 로고
    • Weak quantifier elimination for the full linear theory of the integers. A uniform generalization of Presburger arithmetic
    • Lasaruk, A., Sturm, T.: Weak quantifier elimination for the full linear theory of the integers. A uniform generalization of Presburger arithmetic. Applicable Algebra in Engineering, Communication and Computing 18(6), 545-574 (2007)
    • (2007) Applicable Algebra in Engineering, Communication and Computing , vol.18 , Issue.6 , pp. 545-574
    • Lasaruk, A.1    Sturm, T.2
  • 28
    • 38149052213 scopus 로고    scopus 로고
    • Weak integer quantifier elimination beyond the linear case
    • Ganzha, V. G., Mayr, E. W., Vorozhtsov, E. V. eds., Springer, Heidelberg
    • Lasaruk, A., Sturm, T.: Weak integer quantifier elimination beyond the linear case. In: Ganzha, V. G., Mayr, E. W., Vorozhtsov, E. V. (eds.) CASC 2007. LNCS, vol. 4770, pp. 275-294. Springer, Heidelberg (2007)
    • (2007) CASC 2007. LNCS , vol.4770 , pp. 275-294
    • Lasaruk, A.1    Sturm, T.2
  • 30
    • 84880990802 scopus 로고
    • Compound matrices and ordinary differential equations
    • Muldowney, J. S.: Compound matrices and ordinary differential equations. Rocky Mt. J. Math. 20(4), 857-872 (1990)
    • (1990) Rocky Mt. J. Math. , vol.20 , Issue.4 , pp. 857-872
    • Muldowney, J.S.1
  • 31
    • 78049401425 scopus 로고    scopus 로고
    • Algorithmic global criteria for excluding oscillations
    • Accepted for publication. Special issue on "Algebraic Biology"
    • Weber, A., Sturm, T., Abdel-Rahman, E. O.: Algorithmic global criteria for excluding oscillations. Bulletin of Mathematical Biology (2010); Accepted for publication. Special issue on "Algebraic Biology"
    • (2010) Bulletin of Mathematical Biology
    • Weber, A.1    Sturm, T.2    Abdel-Rahman, E.O.3
  • 33
    • 0023242792 scopus 로고
    • Bendixson-type theorems with applications
    • Tóth, J.: Bendixson-type theorems with applications. Z. Angew. Math. Mech. 67, 31-35 (1987)
    • (1987) Z. Angew. Math. Mech. , vol.67 , pp. 31-35
    • Tóth, J.1
  • 35
    • 1542617059 scopus 로고    scopus 로고
    • On the behavior of solutions in viral dynamical models
    • Tuckwell, H. C., Wan, F. Y. M.: On the behavior of solutions in viral dynamical models. BioSystems 73(3), 157-161 (2004)
    • (2004) BioSystems , vol.73 , Issue.3 , pp. 157-161
    • Tuckwell, H.C.1    Wan, F.Y.M.2
  • 36
    • 0031000756 scopus 로고    scopus 로고
    • Human immunodeficiency virus drug therapy and virus load
    • Bonhoeffer, S., Coffin, J. M., Nowak, M. A.: Human immunodeficiency virus drug therapy and virus load. The Journal of Virology 71(4), 3275 (1997)
    • (1997) The Journal of Virology , vol.71 , Issue.4 , pp. 3275
    • Bonhoeffer, S.1    Coffin, J.M.2    Nowak, M.A.3
  • 37
    • 33646842048 scopus 로고    scopus 로고
    • A generalization of Bendixson's criterion
    • DOI 10.1090/S0002-9939-01-06107-X
    • Feckan, M.: A generalization of Bendixson's criterion. Proceedings American Mathematical Society 129(11), 3395-3400 (2001) (Pubitemid 33346439)
    • (2001) Proceedings of the American Mathematical Society , vol.129 , Issue.11 , pp. 3395-3400
    • Feckan, M.1
  • 38
    • 68749105659 scopus 로고    scopus 로고
    • A semi-algebraic approach for asymptotic stability analysis
    • She, Z., Xia, B., Xiao, R., Zheng, Z.: A semi-algebraic approach for asymptotic stability analysis. Nonlinear Analysis: Hybrid Systems 3(4), 588-596 (2009)
    • (2009) Nonlinear Analysis: Hybrid Systems , vol.3 , Issue.4 , pp. 588-596
    • She, Z.1    Xia, B.2    Xiao, R.3    Zheng, Z.4
  • 39
    • 0346830372 scopus 로고    scopus 로고
    • Theoretical and numerical analysis of differentialalgebraic equations
    • Ciarlet, P. G., Lions, J. L. eds., North-Holland, Amsterdam
    • Rabier, P. J., Rheinboldt, W. C.: Theoretical and numerical analysis of differentialalgebraic equations. In: Ciarlet, P. G., Lions, J. L. (eds.) Handbook of Numerical Analysis, vol. VIII, pp. 183-540. North-Holland, Amsterdam (2002)
    • (2002) Handbook of Numerical Analysis , vol.8 , pp. 183-540
    • Rabier, P.J.1    Rheinboldt, W.C.2
  • 41
    • 77956285103 scopus 로고    scopus 로고
    • Involution - The formal theory of differential equations and its applications in Computer Algebra
    • Springer, Berlin
    • Seiler, W. M.: Involution - The Formal Theory of Differential Equations and its Applications in Computer Algebra. In: Algorithms and Computation in Mathematics, vol. 24. Springer, Berlin (2009)
    • (2009) Algorithms and Computation in Mathematics , vol.24
    • Seiler, W.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.