D. S. Arnon, Algorithms for the geometry of semi-algebraic sets, 1981.

S. Basu, R. Pollack, and M. Roy, On the combinatorial and algebraic complexity of quantifier elimination, Journal of the ACM, vol.43, issue.6, pp.1002-1045, 1996.
DOI : 10.1145/235809.235813

F. Boulier, M. Lefranc, F. Lemaire, P. Morant, and A. Ürgüplü, On Proving the Absence of Oscillations in Models of Genetic Circuits, Proceedings of the AB 2007, pp.66-80, 2007.
DOI : 10.1007/978-3-540-73433-8_6
URL : https://hal.archives-ouvertes.fr/hal-00139667

F. Boulier, M. Lefranc, F. Lemaire, and P. Morant, Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits, Proceedings of the AB 2008, pp.56-64, 2008.
DOI : 10.1007/978-3-540-85101-1_5
URL : https://hal.archives-ouvertes.fr/hal-00825126

C. W. Brown and C. Gross, Efficient Preprocessing Methods for Quantifier Elimination, Proceedings of the CASC 2006, pp.89-100, 2006.
DOI : 10.1007/11870814_7

C. W. Brown, QEPCAD B, ACM SIGSAM Bulletin, vol.37, issue.4, pp.97-108, 2003.
DOI : 10.1145/968708.968710

C. W. Brown and M. Ko?ta, Constructing a single cell in cylindrical algebraic decomposition, Journal of Symbolic Computation, vol.70, pp.14-48, 2014.
DOI : 10.1016/j.jsc.2014.09.024
URL : https://hal.archives-ouvertes.fr/hal-01088452

B. Buchberger, Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal . Doctoral dissertation, Mathematical Institute, 1965.

S. Chou, Mechanical Geometry Theorem Proving Mathematics and Its Applications, 1988.
DOI : 10.1007/978-94-009-4037-6

B. L. Clarke, Stability of Complex Reaction Networks, Advances in Chemical Physics, 1980.
DOI : 10.1002/9780470142622.ch1

G. E. Collins, Quantifier elimination for real closed fields by cylindrical algebraic decomposition--preliminary report, Proc. EUROSAM '74, pp.80-90, 1974.
DOI : 10.1145/1086837.1086852

G. E. Collins, Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition, Automata Theory and Formal Languages. 2nd GI Conference, pp.134-183, 1975.

G. E. Collins, Quantifier Elimination by Cylindrical Algebraic Decomposition ??? Twenty Years of Progress, Quantifier Elimination and Cylindrical Algebraic Decomposition, pp.8-23, 1998.
DOI : 10.1007/978-3-7091-9459-1_2

G. E. Collins and H. Hong, Partial Cylindrical Algebraic Decomposition for quantifier elimination, Journal of Symbolic Computation, vol.12, issue.3, pp.299-328, 1991.
DOI : 10.1016/S0747-7171(08)80152-6
URL : https://doi.org/10.1016/s0747-7171(08)80152-6

J. H. Davenport and J. Heintz, Real quantifier elimination is doubly exponential, Journal of Symbolic Computation, vol.5, issue.1-2, pp.29-35, 1988.
DOI : 10.1016/S0747-7171(88)80004-X
URL : https://doi.org/10.1016/s0747-7171(88)80004-x

M. Davis, Mathematical Procedures for Decision Problems. Final Report on Ordnance Research and Development Project No, pp.2-3, 1954.

A. Dolzmann and T. Sturm, Redlog User Manual, 1999.

A. Dolzmann, T. Sturm, and V. Weispfenning, A new approach for automatic theorem proving in real geometry, Journal of Automated Reasoning, vol.21, issue.3, pp.357-380, 1998.
DOI : 10.1023/A:1006031329384

A. Dolzmann and T. Sturm, REDLOG, ACM SIGSAM Bulletin, vol.31, issue.2, pp.2-9, 1997.
DOI : 10.1145/261320.261324

A. Dolzmann and T. Sturm, Simplification of Quantifier-free Formulae over Ordered Fields, Journal of Symbolic Computation, vol.24, issue.2, pp.209-231, 1997.
DOI : 10.1006/jsco.1997.0123

H. Errami, M. Eiswirth, D. Grigoriev, W. M. Seiler, T. Sturm et al., Efficient Methods to Compute Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates, Proceedings of the CASC 2013, pp.88-99, 2013.
DOI : 10.1007/978-3-319-02297-0_7
URL : https://hal.archives-ouvertes.fr/hal-00931946

H. Errami, W. M. Seiler, M. Eiswirth, and A. Weber, Computing Hopf Bifurcations in Chemical Reaction Networks Using Reaction Coordinates, Proceedings of the CASC 2012, 2012.
DOI : 10.1007/978-3-642-32973-9_8
URL : http://www.mathematik.uni-kassel.de/~seiler/Papers/PDF/CASC2012.pdf

H. Errami, M. Eiswirth, D. Grigoriev, W. M. Seiler, T. Sturm et al., Detection of Hopf bifurcations in chemical reaction networks using convex coordinates, Journal of Computational Physics, vol.291, pp.279-302, 2015.
DOI : 10.1016/j.jcp.2015.02.050
URL : https://hal.archives-ouvertes.fr/hal-01239486

G. F. Fussmann, S. P. Ellner, K. W. Shertzer, and N. G. Hairston-jr, Crossing the Hopf Bifurcation in a Live Predator-Prey System, Science, vol.290, issue.5495, pp.1358-1360, 2000.
DOI : 10.1126/science.290.5495.1358

K. Gatermann, M. Eiswirth, and A. Sensse, Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems, Journal of Symbolic Computation, vol.40, issue.6, pp.1361-1382, 2005.
DOI : 10.1016/j.jsc.2005.07.002
URL : https://doi.org/10.1016/j.jsc.2005.07.002

D. N. Godbole and J. Lygeros, Longitudinal control of the lead car of a platoon, IEEE Transactions on Vehicular Technology, vol.43, issue.4, pp.1125-1135, 1994.
DOI : 10.1109/25.330177

D. Grigoriev, Complexity of deciding Tarski algebra, Journal of Symbolic Computation, vol.5, issue.1-2, pp.65-108, 1988.
DOI : 10.1016/S0747-7171(88)80006-3

S. Gulwani and A. Tiwari, Constraint-Based Approach for Analysis of Hybrid Systems, Proceedings of the CAV 2008, pp.190-203, 2008.
DOI : 10.1007/978-3-540-70545-1_18

D. Hilbert, Grundlagen der Geometrie, 1987.

H. Hong, Comparison of several decision algorithms for the existential theory of the reals, 1991.

H. Hong, R. Liska, and S. Steinberg, Testing Stability by Quantifier Elimination, Journal of Symbolic Computation, vol.24, issue.2, pp.161-187, 1997.
DOI : 10.1006/jsco.1997.0121

M. Jirstrand, Cylindrical algebraic decomposition?an introduction, 1995.

M. Kahoui, . El, and A. Weber, Deciding Hopf Bifurcations by Quantifier Elimination in a Software-component Architecture, Journal of Symbolic Computation, vol.30, issue.2, pp.161-179, 2000.
DOI : 10.1006/jsco.1999.0353
URL : https://doi.org/10.1006/jsco.1999.0353

D. Kapur, Using Gr??bner bases to reason about geometry problems, Journal of Symbolic Computation, vol.2, issue.4, pp.399-408, 1986.
DOI : 10.1016/S0747-7171(86)80007-4
URL : https://doi.org/10.1016/s0747-7171(86)80007-4

M. Ko?ta, New concepts for real quantifier elimination by virtual substitution. Doctoral dissertation, 2016.

M. Ko?ta, T. Sturm, and A. Dolzmann, Better answers to real questions, Journal of Symbolic Computation, vol.74, pp.255-275, 2016.
DOI : 10.1016/j.jsc.2015.07.002

B. A. Kutzler and S. Stifter, On the application of Buchberger's algorithm to automated geometry theorem proving, Journal of Symbolic Computation, vol.2, issue.4, pp.389-397, 1986.
DOI : 10.1016/S0747-7171(86)80006-2

W. Liu, Criterion of Hopf Bifurcations without Using Eigenvalues, Journal of Mathematical Analysis and Applications, vol.182, issue.1, pp.250-256, 1994.
DOI : 10.1006/jmaa.1994.1079
URL : https://doi.org/10.1006/jmaa.1994.1079

R. Loos and V. Weispfenning, Applying Linear Quantifier Elimination, The Computer Journal, vol.36, issue.5, pp.450-462, 1993.
DOI : 10.1093/comjnl/36.5.450
URL : https://academic.oup.com/comjnl/article-pdf/36/5/450/1105730/360450.pdf

S. Mccallum, An improved projection operation for cylindrical algebraic decomposition of three-dimensional space, Journal of Symbolic Computation, vol.5, issue.1-2, pp.141-161, 1988.
DOI : 10.1016/S0747-7171(88)80010-5

N. F. Mcphee, S. Chou, and X. Gao, Mechanically proving geometry theorems using a combination of Wu's method and Collins' method, Proceedings of CADE-12, pp.401-415, 1994.
DOI : 10.1007/3-540-58156-1_28

M. Mincheva and M. R. Roussel, Graph-theoretic methods for the analysis of chemical and biochemical networks. I. Multistability and oscillations in ordinary differential equation models, Journal of Mathematical Biology, vol.29, issue.1, pp.61-86, 2007.
DOI : 10.1007/978-1-4612-0601-9

W. Niu and D. Wang, Algebraic Approaches to Stability Analysis of Biological Systems, Mathematics in Computer Science, vol.1, issue.3, pp.507-539, 2008.
DOI : 10.1007/s11786-007-0039-x
URL : https://hal.archives-ouvertes.fr/hal-00588726

B. Novak, Z. Pataki, A. Ciliberto, and J. J. Tyson, Mathematical model of the cell division cycle of fission yeast, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.97, issue.1, pp.277-286, 2001.
DOI : 10.1073/pnas.97.14.7865

S. Prajna, A. Jadbabaie, and G. J. Pappas, A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates, IEEE Transactions on Automatic Control, vol.52, issue.8, pp.1415-1428, 2007.
DOI : 10.1109/TAC.2007.902736
URL : http://www.seas.upenn.edu/~jadbabai/papers/TAC05-Barrier.pdf

A. Prestel, Lectures on formally real fields, Lecture Notes in Mathematics, vol.1093, 1984.
DOI : 10.1007/BFb0101548

A. Puri and P. Varaiya, Driving safely in smart cars, Proceedings of 1995 American Control Conference, ACC'95, 1995.
DOI : 10.1109/ACC.1995.533807
URL : http://paleale.eecs.berkeley.edu/~varaiya/papers_ps.dir/drive.pdf

J. Renegar, On the computational complexity and geometry of the first-order theory of the reals. Part II: The general decision problem. Preliminaries for quantifier elimination, Journal of Symbolic Computation, vol.13, issue.3, pp.301-328, 1992.
DOI : 10.1016/S0747-7171(10)80004-5

J. F. Ritt, Differential Equations from the Algebraic Standpoint, 1932.
DOI : 10.1090/coll/014

J. F. Ritt, Differential Algebra, 1950.
DOI : 10.1090/coll/033

A. Seidenberg, An elimination theory for differential algebra, Univ. Calif. Publ. Math. New Ser, vol.3, issue.2, pp.31-66, 1956.

A. Seidenberg, Some remarks on Hilbert's Nullstellensatz, Archiv der Mathematik, vol.53, issue.4, pp.235-240, 1956.
DOI : 10.1007/BF01900296

A. Seidenberg, On k-constructable sets, k-elementary formulae, and elimination theory. J. für die reine und angewandte Math, pp.239-240, 1969.

A. Seidl and T. Sturm, A generic projection operator for partial cylindrical algebraic decomposition, Proceedings of the 2003 international symposium on Symbolic and algebraic computation , ISSAC '03, pp.240-247, 2003.
DOI : 10.1145/860854.860903
URL : http://www.fmi.uni-passau.de/forschung/mip-berichte/MIP-0301.ps

A. Sensse, M. J. Hauser, and M. Eiswirth, Feedback loops for Shil???nikov chaos: The peroxidase-oxidase reaction, The Journal of Chemical Physics, vol.372, issue.1, pp.14901-14902, 2006.
DOI : 10.1088/0951-7715/11/6/005

T. Sturm and A. Tiwari, Verification and synthesis using real quantifier elimination, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, pp.329-336, 2011.
DOI : 10.1145/1993886.1993935
URL : http://www.csl.sri.com/users/tiwari/papers/issac2011.pdf

T. Sturm and A. Weber, Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology, Proceedings of the AB 2008, pp.200-215, 2008.
DOI : 10.1007/978-3-540-85101-1_15
URL : http://www.risc.uni-linz.ac.at/about/conferences/ab2008/prelim/51470202.pdf

T. Sturm and V. Weispfenning, Computational geometry problems in REDLOG, pp.58-86, 1998.
DOI : 10.1007/BFb0022720
URL : http://www.fmi.uni-passau.de/forschung/mip-berichte/MIP-9708.ps.gz

T. Sturm and V. Weispfenning, Rounding and blending of solids by a real elimination method, Proceedings of the IMACS World Congress, pp.727-732, 1997.

T. Sturm, An Algebraic Approach to Offsetting and Blending of Solids, Proceedings of the CASC 2000, pp.367-382, 2000.
DOI : 10.1007/978-3-642-57201-2_28

T. Sturm, New Domains for Applied Quantifier Elimination, Proceedings of the CASC 2006, 2006.
DOI : 10.1007/11870814_25

T. Sturm, Real Quantifier Elimination in Geometry. Doctoral dissertation, 1999.

T. Sturm, Subtropical Real Root Finding, Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15, pp.347-354, 2015.
DOI : 10.1007/s11538-010-9618-0
URL : https://hal.archives-ouvertes.fr/hal-01239489

T. Sturm, A. Weber, E. O. Abdel-rahman, and M. Kahoui, Investigating Algebraic and Logical Algorithms to Solve Hopf Bifurcation Problems in Algebraic Biology, Mathematics in Computer Science, vol.2, issue.3, pp.493-515, 2009.
DOI : 10.1007/s11786-008-0067-1

A. Tarski, A decision method for elementary algebra and geometry. Prepared for publication by, p.RAND, 1948.
DOI : 10.1007/978-3-7091-9459-1_3

A. Tiwari, Approximate Reachability for Linear Systems, Proceedings of the HSCC 2003, pp.514-525, 2003.
DOI : 10.1007/3-540-36580-X_37
URL : http://www.csl.sri.com/~tiwari/papers/hscc03-1.ps

J. J. Tyson, K. Chen, and B. Novak, MILESTONESNETWORK DYNAMICS AND CELL PHYSIOLOGY, Nature Reviews Molecular Cell Biology, vol.2, issue.12, pp.908-916, 2001.
DOI : 10.1038/35103078

C. Wagner and R. Urbanczik, The Geometry of the Flux Cone of a Metabolic Network, Biophysical Journal, vol.89, issue.6, pp.3837-3845, 2005.
DOI : 10.1529/biophysj.104.055129

D. Wang, Reasoning about Geometric Problems using an Elimination Method, pp.147-185, 1995.
DOI : 10.1007/978-3-7091-6604-8_8

D. Wang, An Elimination Method for Polynomial Systems, Journal of Symbolic Computation, vol.16, issue.2, pp.83-114, 1993.
DOI : 10.1006/jsco.1993.1035
URL : https://doi.org/10.1006/jsco.1993.1035

A. Weber, T. Sturm, and E. O. Abdel-rahman, Algorithmic Global Criteria for Excluding Oscillations, Bulletin of Mathematical Biology, vol.24, issue.2, pp.899-916, 2011.
DOI : 10.1007/978-3-642-57201-2_32

V. Weispfenning, The complexity of linear problems in fields, Journal of Symbolic Computation, vol.5, issue.1-2, pp.3-27, 1988.
DOI : 10.1016/S0747-7171(88)80003-8

V. Weispfenning, Quantifier Elimination for Real Algebra -- the Quadratic Case and Beyond, Applicable Algebra in Engineering, Communication and Computing, vol.8, issue.2, pp.85-101, 1997.
DOI : 10.1007/s002000050055
URL : http://www.fmi.uni-passau.de/~redlog/paper/quadqe1.ps.Z

W. Wu, BASIC PRINCIPLES OF MECHANICAL THEOREM PROVING IN ELEMENTARY GEOMETRIES, J. Syst. Sci. Math. Sci, vol.4, issue.3, pp.207-235, 1984.
DOI : 10.1142/9789812791085_0012

W. Wu, BASIC PRINCIPLES OF MECHANICAL THEOREM PROVING IN ELEMENTARY GEOMETRIES, J. Autom. Reason, vol.2, issue.3, pp.219-252, 1986.
DOI : 10.1142/9789812791085_0012