[1] Poincaré H. Mémoire sur les courbes définies par une équation différentielle (I), (II). Journal de Mathématiques Pures et Appliquées, 1881, 7: 375-422; 1882, 8: 251-296; 1885, 1: 167-244
[2] Liapunov A. The General Problem of the Stability of Motion. Kharkov: Kharkov Mathematical Society, 1892
[3] Nemitskij V, Stepanov V. Qualitative Theory of Differential Equations. Princeton: Princeton University Press, 1960
[4] Zhang Z, Ding T, Huang W, Dong Z. Qualitative Theory of Differential Equations. Providence, RI: American Mathematical Society, 1992
[5] Qin Y, Zhang J, Qin C. Computer deduction of stability criteria for a class of nonlinear systems. J Qufu Normal University, 1985, 2: 1-11(in Chinese)
[6] Wang D. Mechanical manipulation for a class of differential systems. J Symbolic Comput, 1991, 12: 233-254
[7] Wu W-T. Basic principles of mechanical theorem proving in elementary geometries. J Sys Sci & Math Sci, 1984, 4: 207-235; J Automat Reasoning, 1986, 2: 221-252
[8] Buchberger B. Gröbner bases: An algorithmic method in polynomial ideal theory//Bose N K, Ed. Multidimensional Systems Theory. Reidel: Dordrecht, 1985: 184-232
[9] Jin X, Wang D. On the conditions of Kukles for the existence of a centre. Bull London Math Soc, 1990, 22: 1-4
[10] Christopher C, Lloyd N. On the paper of Jin and Wang concerning the conditions for a center in certain cubic systems. Bull London Math Soc, 1990, 22: 5-12
[11] Lloyd N, Pearson J. Computing centre conditions for certain cubic systems. J Comput Appl Math, 1992, 40: 323-336
[12] Christopher C. Invariant algebraic curves and conditions for a centre. Proc R Soc Edinb Sect A, 1994, 124: 1209-1229
[13] Ye W, Ye Y. Qualitative theory of the Kukles systems: (I) number of critical points. Ann Differ Equations, 2001, 17: 275-286
[14] Pearson J, Lloyd N. Kukles revisited: Advances in computing techniques. Comput Math Appl, 2010, 60: 2797-2805
[15] Hong H, Liska R, Steinberg S. Testing stability by quantifier elimination. J Symbolic Comput, 1997, 24: 161-187
[16] Wang D, Xia B. Stability analysis of biological systems with real solution classification//Gao X-S, Labahn G, Ed. Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation. New York: ACM Press, 2005: 354-361
[17] Hong H, Tang X, Xia B. Special algorithm for stability analysis of multistable biological regulatory systems. J Symbolic Comput, 2015, 70: 112-135
[18] Pearson J, Lloyd N, Christopher C. Algorithmic derivation of centre conditions. SIAM Rev, 1996, 38: 619-636
[19] Romanovski V, Shafer D. The Center and Cyclicity Problems: A Computational Algebra Approach. Boston, MA: Birkhäuser Boston Inc, 2009
[20] Romanovski V. Computational algebra and limit cycles bifurcations in polynomial systems. Nonlinear Phenom Complex Syst, 2007, 10: 79-85
[21] Chen C, Corless R, Moreno Maza M, Yu P, Zhang Y. An application of regular chain theory to the study of limit cycles. Int J Bifurcation Chaos, 2013, 23: 1350154-1-23
[22] Sun X, Huang W. Bounding the number of limit cycles for a polynomial Liénard system by using regular chains. J Symbolic Comput, 2017, 79: 197-210
[23] Buchberger B. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal [D]. Austria: Universität Innsbruck, 1965
[24] Faugère J-C, Gianni P, Lazard D, et al. Efficient computation of zero-dimensional Gröbner bases by change of ordering. J Symbolic Comput, 1993, 16: 329-344
[25] Faugère J-C, Mou C. Sparse FGLM algorithms. J Symbolic Comput, 2017, 80: 538-569
[26] Faugère J-C. A new efficient algorithm for computing Gröbner bases (F4). J Pure Appl Algebra, 1999, 139: 61-88, 1999
[27] Faugère J-C. A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)//Giusti M, Ed. Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation. New York: ACM Press, 2002: 75-83
[28] Wu W-T. Mathematics Mechanization. Beijing: Science Press/Kluwer Academic, 2000
[29] Ritt J. Differential Algebra. New York: American Mathematical Society, 1950
[30] Aubry P, Lazard D, Moreno Maza M. On the theories of triangular sets. J Symbolic Comput, 1999, 28: 105-124
[31] Wang D. Elimination Methods. New York: Springer-Verlag, 2001
[32] Cox D, Little J, O’Shea D. Using Algebraic Geometry. New York: Springer, 2005
[33] Collins G. Quantifier elimination for real closed fields by cylindrical algebraic decomposition//Barkhage H, Ed. Proceedings of the Second GI Conference on Adtomata Theory and Formal Languages. Berlin Heidelberg: Springer, 1975: 134-183
[34] Collins G, Hong H. Partial cylindrical algebraic decomposition for quantifier elimination. J Symbolic Comput, 1991, 12: 299-328
[35] Yang L, Hou X, Xia B. A complete algorithm for automated discovering of a class of inequality-type theorems. Sci China Ser F, 2001, 44: 33-49
[36] Yang L, Xia B. Real solution classifications of parametric semi-algebraic systems//Dolzmann A, Seidl A, Sturm T, Ed. Algorithmic Algebra and Logic - Proceedings of the A3L 2005. Norderstedt: Herstellung und Verlag, 2005: 281-289
[37] Lazard D, Rouillier F. Solving parametric polynomial systems. J Symbolic Comput, 2007, 42: 636-667
[38] Wang D. Computational polynomial algebra and its biological applications//Anai H, Horimoto K, Ed. Proceedings of the First International Conference on Algebraic Biology (AB 2005). Tokyo: Universal Academy Press, Inc, 2005: 127-137
[39] Miller R, Michel A. Ordinary Differential Equations. New York: Academic Press, 1982
[40] Liénard A, Chipart M. Sur le signe de la partie réelle des racines d’une équation algébrique. J Math Pure Appl, 1914, 10: 291-346
[41] Niu W, Wang D. Algebraic approaches to stability analysis of biological systems. Math Comput Sci, 2008, 1: 507-539
[42] Jirstrand M. Nonlinear control system design by quantifier elimination. J Symbolic Comput, 1997, 24: 137-152
[43] She Z, Xia B, Xiao R, et al. A semi-algebraic approach for asymptotic stability analysis. Nonlinear Anal, 2009, 3: 588-596
[44] She Z, Li H, Xue B, et al. Discovering polynomial Lyapunov functions for continuous dynamical systems. J Symbolic Comput, 2013, 58: 41-63
[45] Niu W, Wang D. Algebraic analysis of stability and bifurcation of a self-assembling micelle system. Appl Math Comput, 2012, 219: 108-121
[46] Khibnik A. LINLBF: A program for continuation and bifurcation analysis of equilibria up to codimension three//Roose D, Ed. Continuation and Bifurcation: Numerical Techniques and Applications. Norwell, MA: Kluwer Academic Publishers, 1990: 283-296
[47] Guckenheimer J, Myers M, Sturmfels B. Computing Hopf bifurcation I. SIAM J Numer Anal, 1997, 34: 1-21
[48] Guckenheimer J, Myers M. Computing Hopf bifurcations. II: Three examples from neurophysiology. SIAM J Sci Comput, 1996, 17: 1-27
[49] Moore G, Garrett T, Spence A. The numerical detection of Hopf bifurcation points//Roose D, Ed. Continuation and Bifurcation: Numerical Techniques and Applications. Norwell, MA: Kluwer Academic Publishers, 1990: 227-246
[50] Roose D. An algorithm for the computation of Hopf bifurcation points in comparison with other methods. J Comput Appl Math, 1985, 12: 517-529
[51] Liu W. Criterion of Hopf bifurcations without using eigenvalues. J Math Anal Appl, 1994, 182: 250-256
[52] El Kahoui M, Weber A. Deciding Hopf bifurcations by quantifier elimination in a software-component architecture. J Symbolic Comput, 2000, 30: 161-179
[53] Shahruz S, Kalkin D. Limit cycle behavior in three or higher dimensional nonlinear systems: The Lotka- Volterra example//Dieulot J, Richard J, Ed. Proceedings of the 40th IEEE Conference on Decision and Control. Orlando: IEEE, 2001: 379-386
[54] Kuznetsov Y. Elements of Applied Bifurcation Theory. New York: Springer-Verlag, 2004
[55] Chow S-N, Hale J. Methods of Bifurcation Theory. New York: Springer, 1982
[56] Govaerts W, Guckenheimer J, Khibnik A. Defining functions for multiple Hopf bifurcations. SIAM J Numer Anal, 1997, 34: 1269-1288
[57] Liapunov A. Probléme Général de la Stabilité du Mouvement. New Jersey: Princeton University Press, 1947
[58] Giné J, Santallusia X. Implementation of a new algorithm of computation of the Poincaré-Liapunov constants. J Comput Appl Math, 2004, 166: 465-476
[59] Lynch S. Symbolic computation of Lyapunov quantities and the second part of Hilbert’s sixteenth problem//Wang D, Zheng Z, Ed. Differential Equations with Symbolic Computation. Basel: Birkhäuser, 2005: 1-22
[60] Yu P, Chen G. Computation of focus values with applications. Nonlinear Dyn, 2008, 51: 409-427
[61] Shi S. A method of constructing cycles without contact around a weak focus. J Differential Equations, 1981, 41: 301-312
[62] Giné J. On some open problems in planar differential systems and Hilbert’s 16th problem. Chaos Solitons & Fractals, 2007, 31: 1118-1134
[63] Żoladek H. On certain generalization of the Bautin’s theorem. Nonlinearity, 1994, 7: 273-279
[64] Żoladek H. The classification of reversible cubic systems with center. Topol Methods Nonlinear Anal, 1994, 4: 79-136
[65] Dulac H. Détermination et intégration d’une certaine classe d’équations différentielles ayant pour point singulier un center. Bull Sci Math, 1908, 32: 230-252
[66] Bautin N. On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type. Mat Sb, 1952, 30: 181-196(in Russian); Amer Math Soc Transl, 1954, 100: 397-413
[67] Sibirskii K. On the number of limit cycles in the neighbourhood of a singular point. Differential Equations, 1965, 1: 36-47
[68] Kukles I. Sur quelques cas de distinction entre un foyer et un centre. Dokl Akad Nauk SSSR, 1944, 42: 208-211
[69] Cherkas L. Conditions for the equation $yy'=\sum\limits_{i=0}^3p_i(x)y^i$ to have a center. Differentsial’nye Uravneniya, 1978, 14: 1594-1600
[70] Wang D. Polynomial systems from certain differential equations. J Symbolic Comput, 1999, 28: 303-315
[71] Sadovskii A. Solutions of the center and focus problem for a cubic system of nonlinear oscillations. Differential Equations, 1997, 33: 236-244
[72] Wang D. An elimination method for polynomial systems. J Symbolic Comput, 1993, 16: 83-114
[73] Lu Z, Ma S. Centers, foci, and limit cycles for polynomial differential systems//Gao X-S, Wang D, Ed. Mathematics Mechanization and Applications. London: Academic Press, 2000: 365-387
[74] Giné J. Center conditions for generalized polynomial Kukles systems. Commun Pur Appl Anal, 2017, 16: 417-425
[75] Chavarriga J, Giné J. Integrability of a linear center perturbed by fourth degree homogeneous polynomial. Publ Mat, 1996, 40: 21-39
[76] Chavarriga J, Giné J. Integrability of a linear center perturbed by fifth degree homogeneous polynomial.Publ Mat, 1997, 41: 335-356
[77] Giné J, Llibre J, Valls C. Centers for the Kukles homogeneous systems with odd degree. Bull London Math Soc, 2015, 47: 315-324
[78] Giné J, Llibre J, Valls C. Centers for the Kukles homogeneous systems with even degree. J Appl Anal Comput, 2017, 7: 1534-1548
[79] Schlomiuk D. Algebraic particular integrals, integrability and the problem of center. Trans Am Math Soc, 1993, 338: 799-841
[80] Edneral V, Mahdi A, Romanovski V, et al. The center problem on a center manifold in R3. Nonlinear Anal, 2012, 75: 2614-2622
[81] Mahdi A. The center problem for the third-order ODEs. Internat J Bifur Chaos, 2013, 23: 1350078-1-11
[82] Mahdi A, Pessoa C, Hauenstein J. A hybrid symbolic-numerical approach to the center-focus problem. J Symbolic Comput, 2017, 82: 57-73
[83] Romanovski V, Xia Y, Zhang X. Varieties of local integrability of analytic differential systems and their applications. J. Differential Equations, 2014, 257: 3079-3101
[84] Conti R. Centers of planar polynomial systems. A review. Le Matematiche, 1998, 53: 207-240
[85] Chavarriga J, Sabatini M. A survey of isochronous centers. Qual Theory Dyn Syst, 1999, 1: 1-70
[86] Hilbert D. Mathematical problems. Bull Amer Math Soc, 1902, 8: 437-479
[87] Dulac H. Sur les cycles limites. Bull Soc Math France, 1923, 51: 45-188
[88] Otrokov N. On the number of limit cycles of a differential equation in the neighborhood of a singular point. Mat Sbornik, 1954, 34: 127-144
[89] Écalle J. Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Actualitiées Math. Paris: Hermann, 1992
[90] Ilyashenko Yu. Finiteness theorems for limit cycles. Uspekhi Mat Nauk, 1990, 2: 143-200(Russian); English transl Russian Math Surveys 1990, 45: 129-203
[91] Christopher C. Estimating limit cycle bifurcations from centers//Wang D, Zheng Z, Ed. Differential Equations with Symbolic Computation. Basel: Birkhäuser, 2005: 23-35
[92] Chen L, Wang M. The relative position, and the number, of limit cycles of a quadratic differential system. Acta Math Sinica, 1979, 22: 751-758
[93] Li C, Liu C, Yang J. A cubic system with thirteen limit cycles. J Differential Equations, 2009, 246: 3609-3619
[94] Bamon R. The solution of Dulac’s problem for quadratic vector fields. Ann Acad Bros Cienc, 1985, 57: 111-142
[95] Christopher C, Lloyd N. Polynomial systems: A lower bound for the Hilbert numbers. Proc Royal Soc London Ser A, 1995, 450: 219-224
[96] Han M, Li J. Lower bounds for the Hilbert number of polynomial systems. J Differential Equations, 2012, 252: 3278-3304
[97] Han M, Shang D, Wang Z, et al. Bifurcation of limit cycles in a 4th-order near-Hamiltonian polynomial systems. Internat J Bifur Chaos, 2007, 11: 4117-4144
[98] Sun X, Han M. On the number of limit cycles of a Z4-equivariant quintic near-Hamiltonian system. Acta Math Sin, Engl Ser, 2015, 31: 1805-1824
[99] Wu Y, Wang X, Tian L. Bifurcations of limit cycles in a Z4-equivariant quintic planar vector field. Acta Math Sin, Engl Ser, 2010, 26: 779-798
[100] Wang S, Yu P. Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation. Chaos Solitons & Fractals, 2005, 26: 1317-1335
[101] Li J. Hilbert’s 16th problem and bifurcations of planar polynomial vector fields. Internat J Bifur Chaos, 2003, 13: 47-106
[102] Wang D. A class of cubic differential systems with 6-tuple focus. J Differential Equations, 1990, 87: 305-315
[103] Li J, Bai J. The cyclicity of multiple Hopf bifurcation in planar cubic differential systems: M(3) ≥ 7. Science Bulletin, 1990, 23: 2016-2017
[104] James E, Lloyd N. A cubic system with eight small-amplitude limit cycles. IMA J Appl Math, 1991, 47: 163-171
[105] Ning S, Ma S, Kwek K, et al. A cubic system with eight small-amplitude limit cycles. Appl Math Lett, 1994, 7: 23-27
[106] Yu P, Corless R. Symbolic computation of limit cycles associated with Hilbert’s 16th problem. Commun Nonlinear Sci Numer Simul, 2009, 14: 4041-4056
[107] Zhang W, Hou X, Zeng Z. Weak centers and bifurcation of critical periods in reversible cubic systems. Comput Math Appl, 2000, 40: 771-782
[108] Lu Z, Luo Y. Two limit cycles in three-dimensional Lotka-Volterra systems. Comput Math Appl, 2002, 44: 51-66
[109] Wang D, Zheng Z. Differential Equations with Symbolic Computation. Basel: Birkhäuser, 2005
[110] Chen C, Moreno Maza M. Semi-algebraic description of the equilibria of dynamical systems//Gerdt V, Koepf W, Mayr E, et al, Ed. Computer Algebra in Scientific Computing. Heidelberg: Springer, 2011: 101-125
[111] Lloyd N, Pearson J. A cubic differential system with nine limit cycles. J Appl Anal Comput, 2012, 2: 293-304
[112] Yu P, Tian Y. Twelve limit cycles around a singular point in a planar cubic-degree polynomial system. Commun Nonlinear Sci Numer Simul, 2014, 19: 2690-2705
[113] Levandovskyy V, Romanovski V, Shafer D. The cyclicity of a cubic system with nonradical Bautin ideal. J Differential Equations, 2009, 246: 1274-1287
[114] Han M, Romanovski V. Estimating the number of limit cycles in polynomial systems. J Math Anal Appl, 2010, 368: 491-497
[115] Han M, Yu P. Normal Forms, Melnikov Functions, and Bifurcations of Limit Cycles. New York: Springer, 2012
[116] Han M, Yang J, Yu P. Hopf bifurcations for near-Hamiltonian systems. Int J Bifurcation Chaos, 2009, 19: 4117-4130
[117] Llibre J, Zhang X. Hopf bifurcation in higher dimensional differential systems via the averaging method. Pacific J Math, 2009, 240: 321-341
[118] Llibre J, Valls C. Hopf bifurcation for some analytic differential systems in R3 via averaging theory. Discrete Contin Dyn Syst, 2011, 30: 779-790
[119] Huang B, Yap C. An algorithmic approach to small limit cycles of nonlinear differential systems: The averaging method revisited. J Symbolic Comput, 2021. DOI: 10.1016/j.jsc.2020.09.001
[120] Yu P. Computation of normal forms via a perturbation technique. J Sound Vib, 1998, 211: 19-38
[121] Bi Q, Yu P. Symbolic computation of normal forms for semi-simple cases. J Comput Appl Math, 1999, 102: 195-220
[122] Zeng B, Yu P. Analysis of zero-Hopf bifurcation in two Rössler systems using normal form theory. Internat J Bifur Chaos, 2020, 30: 2030050-1-14
[123] Tian Y, Yu P. An explicit recursive formula for computing the normal forms associated with semisimple cases. Commun Nonlinear Sci Numer Simul, 2014, 19: 2294-2308
[124] Llibre J, Makhlouf A, Badi S. 3-dimensional Hopf bifurcation via averaging theory of second order. Discrete Contin Dyn Syst, 2009, 25: 1287-1295
[125] Chow S-N, Mallet-Paret J. Hopf bifurcation and the method of averaging//Marsden J, McCracken M, Ed. The Hopf Bifurcation and Its Applications. New York: Springer-Verlag, 1976: 151-162
[126] Llibre J, Novaes D, Teixeira M. Higher order averaging theory for finding periodic solutions via Brouwer degree. Nonlinearity, 2014, 27: 563-583
[127] Huang B, Wang D. Zero-Hopf bifurcation of limit cycles in certain differential systems. 2022, https://arxiv.org/abs/2205.14450
[128] Sanders J, Verhulst F, Murdock J. Averaging Methods in Nonlinear Dynamical Systems. Applied Mathematical Sciences. New York: Springer, 2007
[129] Llibre J, Moeckel R, Simó C. Central Configuration, Periodic Oribits, and Hamiltonian Systems. Advanced Courses in Mathematics-CRM Barcelona, Basel: Birkhäuser, 2015
[130] Pi D, Zhang X. Limit cycles of differential systems via the averaging method. Canad Appl Math Quart, 2009, 7: 243-269
[131] Barreira L, Llibre J, Valls C. Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension. Nonlinear Dynam, 2018, 92: 1159-1166
[132] Blows T, Perko L. Bifurcation of limit cycles from centers and separatrix cycles of planar analytic systems, SIAM Rev, 1994, 36: 341-376
[133] Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields.New York: Springer, 1993
[134] Viano M, Llibre J, Giacomini H. Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor. Nonlinear Anal, 2002, 48: 117-136
[135] Han M, Romanovski V, Zhang X. Equivalence of the Melnikov function method and the averaging method. Qual Theory Dyn Syst, 2016, 15: 471-479
[136] Arnold I. Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. Funct Anal Appl, 1977, 11: 85-92
[137] Christopher C, Li C. Limit Cycles of Differential Equuations. Advanced Courses in Mathematics, CRM Barcelona, Basel: Birkhäuser, 2007
[138] Cveticanin L. Strong Nonlinear Oscillators. Cham: Springer, 2018
[139] Dumortier F, Li C. Perturbations from an elliptic Hamiltonian of degree four: (I) saddle loop and two saddle cycle. J Differential Equations, 2001, 176: 114-157; (II) cuspidal loop. J Differential Equations, 2001, 175: 209-243; (III) global center. J Differential Equations, 2003, 188: 473-511; (IV) figure eightloop. J Differential Equations, 2003, 88: 512-514
[140] Asheghi R, Zangeneh H. Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-gure loop. Nonlinear Anal, 2008, 68: 2957-2976
[141] Asheghi R, Zangeneh H. Bifurcations of limit cycles for a quintic Hamiltonian system with a double cuspidal loop. Comput Math Appl, 2010, 59: 1409-1418
[142] Zhao L. The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle. Nonlinear Anal, 2014, 95: 374-387
[143] Grau M, Mañosas F, Villadelprat J. A Chebyshev criterion for Abelian integrals. Transl Am Math Soc, 2011, 363: 109-129
[144] Mañosas F, Villadelprat J. Bounding the number of zeros of certain Abelian integrals. J Differential Equations, 2011, 251: 1656-1669
[145] Wang J, Xiao D. On the number of limit cycles in samll perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle. J Differential Equations, 2011, 250: 2227-2243
[146] Atabaigi A, Zangeneh H. Bifurcation of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems of degree 5 with a cusp. J Appl Anal Comput, 2011, 1: 299-313
[147] Wang J. Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis. Chaos Solitons & Fractals, 2016, 87: 30-38
[148] Hu Y, Niu W, Huang B. Bounding the number of limit cycles for parametric Liénard systems using symbolic computation methods. Commun Nonlinear Sci Numer Simul, 2021, 96: 105716-1-16
[149] Sun X, Xi H, Zangeneh R, Kazemi R. Bifurcation of limit cycles in small perturbation of a class of Liénard systems. Internat J Bifur Chaos, 2014, 24: 1450004-1-23
[150] Kazemi R, Zangeneh H. Bifurcation of limit cycles in small perturbations of a hyper-elliptic Hamiltonian system with two nilpotent saddles. J Appl Anal Comput, 2012, 2: 395-413
[151] Sun X, Zhao L. Perturbations of a class of hyper-elliptic Hamiltonian systems of degree seven with nilpotent singular points. Appl Math Comput, 2016, 289: 194-203
[152] Sun X, Yu P. Exact bound on the number of zeros of Abelian integrals for two hyper-elliptic Hamiltonian systems of degree 4. J Differential Equations, 2019, 267: 7369-7384
[153] Smith J. Mathematical Ideas in Biology. London: Cambridge University Press, 1968
[154] Smith J. Evolution and the Theory of Games. London: Cambridge University Press, 1982
[155] May R. Simple mathematical models with very complicated dynamics. Nature, 1976, 261: 459-467
[156] Niu W. Qualitative Analysis of Biological Systems Using Algebraic Methods [D]. Paris: Université Paris VI, 2011
[157] Niu W, Wang D. Algebraic analysis of bifurcation and limit cycles for biological systems//Horimoto K, Regensburger G, Rosenkranz M, et al, Ed. Proceedings of the Third International Conference on Algebraic Biology. Heidelberg: Springer-Verlag, 2008: 156-171
[158] Errami H, Eiswirth M, Grigoriev D, et al. Efficient methods to compute Hopf bifurcations in chemical reaction networks using reaction coordinates//Gerdt V, Koepf W, Mayr E, et al, Ed. Computer Algebra in Scientific Computing. Heidelberg: Springer-Verlag, 2013: 88-99
[159] Bradford R, Davenport J, England M, et al. Identifying the parametric occurrence of multiple steady states for some biological networks. J Symbolic Comput, 2020, 98: 84-119
[160] Dickenstein A, Millán M, Shiu A, et al. Multistationarity in structured reaction networks. B Math Biol,2019, 81: 1527-1581
[161] Mou C, Ju W. Sparse triangular decomposition for computing equilibria of biological dynamic systems based on chordal graphs. IEEE/ACM Trans Comput Biol Bioinform, 2022. DOI: 10.1109/TCBB.2022.3156759
[162] Gatermann K, Huber B. A family of sparse polynomial systems arising in chemical reaction systems. J Symbolic Comput, 2022, 33: 275-305
[163] Gatermann K. Counting stable solutions of sparse polynomial systems in chemistry//Green E, Hosten S, Laubenbacher R, et al, Ed. Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering. Providence, RI: American Mathematical Society, 2001: 53-70
[164] Gatermann K, Eiswirth M, Sensse A. Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems. J Symbolic Comput, 2005, 40: 1361-1382
[165] Ferrell J, Machleder E. The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science, 1998, 280: 895-898
[166] Angeli D, Ferrell J, Sontag E. Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proc Nat Acad Sci, 2004, 101: 1822-1827
[167] Liu L, Lu Z, Wang D. The structure of LaSalle’s invariant set for Lotka-Volterra systems. Sci China (Ser A), 1991, 34: 783-790
[168] Lu Z. Computer aided proof for the global stability of Lotka-Volterra systems. Comput Math Appl, 1996, 31: 49-59
[169] Li B, Shen Y, Li B. Quasi-Steady-State laws in enzyme kinetics. J Phys Chem A, 2008, 112: 2311-2321
[170] Li B, Li B. Quasi-Steady-State laws in reversible model of enzyme kinetics. J Math Chem, 2013, 51: 2668-2686
[171] Boulier F, Lemaire F, Sedoglavic A, et al. Towards an automated reduction method for polynomial ODE models in cellular biology. Math Comput Sci, 2009, 2: 443-464
[172] Boulier F, Lazard D, Ollivier F, et al. Representation for the radical of a finitely generated differential ideal//Levelt A, Ed. Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation. New York: ACM Press, 1995: 158-166
[173] Boulier F, Lefranc M, Lemaire F, et al. Model reduction of chemical reaction systems using elimination. Math Comput Sci, 2011, 5: 289-301
[174] Boulier F, Lefranc M, Lemaire F, et al. Applying a rigorous Quasi-Steady State Approximation method for proving the absence of oscillations in models of genetic circuits//Horimoto K, Regensburger G, Ed. Proceedings of the Third International Conference on Algebraic Biology. Heidelberg: Springer-Verlag, 2008: 56-64
[175] Wang D. Algebraic stability criteria and symbolic derivation of stability conditions for feedback control systems. Int J of Control, 2012, 85: 1414-1421
[176] Li X, Wang D. Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification. J Math Econ, 2014, 54: 48-58
[177] Huang B, Niu W. Analysis of snapback repellers using methods of symbolic computation. Int J Bifurcation Chaos, 2019, 29: 1950054-1-13
[178] Quadrat A, Zerz E. Algebraic and Symbolic Computation Methods in Dynamical Systems. Advances in Delays and Dynamics. Cham: Springer, 2020
