Citation: |
[1] |
A. Algaba, E. Friere and E. Gamero, Characterizing and computing normal forms using Lie transforms: A survey, Dyn. Continuous, Discrete Impulsive Systems, 8 (2001), 449-476. |
[2] |
V. I. Arnold, "Geometrical Methods in the Theory of Ordinary Differential Equations," Springer Verlag, New York, 1982. |
[3] |
J. Archuleta, P. Mullens and T. P. Primm, The relationship of temperature to desiccation and starvation tolerance of the Mycobacterium avium complex, Arch. Microbiol., 178 (2002), 311-314.doi: 10.1007/s00203-002-0455-x. |
[4] |
V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, in "Dynamical Systems III, Encyclopaedia Mathematical Science," 2nd ed., Springer-Verlag, New York, 1993. |
[5] |
R. F. M. Bevers, K. H. Kurth and D. J. H. Schamhart, Role of urothelial cells in BCG immuno-therapy for superficial bladder cancer, Brit. J. Cancer, 91 (2004), 607-612. |
[6] |
Y. N. Bibikov, "Local Theory of Nonlinear Analytic Ordinary Differential Equations," Lecture Notes in Mathematics, Springer Verlag, New York, 702 (1979). |
[7] | |
[8] |
A. Bohle and S. Brandau, Immune mechanisms in bacillus CalmetteGuerin immunotherapy for superficial bladder cancer, J. Urol., 170 (2003), 96496.doi: 10.1097/01.ju.0000073852.24341.4a. |
[9] |
A. D. Bruno, "Local Methods in Nonlinear Diff. Equations," Springer Verlag, New York, 1989. |
[10] |
S. Bunimovich-Mendrazitsky, E. Shochat and L. Stone, Mathematical Model of BCG Immunotherapy in Superficial Bladder Cancer, Bull. Math. Biol., 69 (2007), 1847-1870.doi: 10.1007/s11538-007-9195-z. |
[11] |
S. Bunimovich-Mendrazitsky, H. M. Byrne and L. Stone, Mathematical Model of Pulsed Immunotherapy for Superficial Bladder Cancer, Bull. Math. Biol., 70 (2008), 2055-276.doi: 10.1007/s11538-008-9344-z. |
[12] |
C. W. Cheng, M. T. Ng, S. Y. Chan and W. H. Sun, Low dose BCG as adjuvant therapy for superficial bladder cancer and literature review, Anz Journal of Surgery, 74 (2004), 569-572.doi: 10.1111/j.1445-2197.2004.02941.x. |
[13] |
S. N. Chow and J. K. Hale, "Methods of Bifurcation Theory," New York: Springer, 1982. |
[14] |
S. N. Chow, C. Li and D. Wang, "Normal Forms and Bifurcations of Planar Vector Fields," Cambridge University Press, Cambridge, 1994.doi: 10.1017/CBO9780511665639. |
[15] |
Y. M. Goltser, On the strong stability of resonance systems with parametrical perturbations, Applied Mathematics and Mechanics (PMM), Acad. Sc. USSR, 41 (1977), 251-261. |
[16] |
Y. M. Goltser, Bifurcation and stability of neutral systems in the neighborhood of third order resonance, Applied Mathematics and Mechanics (PMM), Acad. Sc. USSR, 43 (1979), 429-440. |
[17] |
Y. M. Goltser, On the extent of proximity of neutral systems to internal resonance, Applied Mathematics and Mechanics (PMM), Acad. Sc. USSR, 50 (1986), 945-954. |
[18] |
Y. M. Goltser, Some bifurcation problems of stability, Nonlinear Analysis, TMA, 30 (1997), 1461-1467.doi: 10.1016/S0362-546X(97)00044-8. |
[19] |
J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields," Applied Mathematical Sciences, New York: Springer, 1983. |
[20] |
G. Iooss and M. Adelmeyer, "Topics in Bifurcation Theory and Applications," World Scientific, Singapore, 1992. |
[21] |
A. Jemal, T. Murray, E. Ward, A. Samuels, R. C. Tiwari, A. Ghafoor, E. J. Feuer and M. J. Thun, Cancer Statistics, CA Cancer. J. Clin., 55 (2005), 10-30.doi: 10.3322/canjclin.55.1.10. |
[22] |
F. A. Kelley, The stable, center stable, center, center unstable, and unstable manifolds, J. Diff. Eqns, 3 (1967), 546-570.doi: 10.1016/0022-0396(67)90016-2. |
[23] |
V. A. Kuznetsov, I. A. Makalkin, M. A. Taylor and A. S. Perelson, Nonlinear dynamics of immunogenic tumours: Parameter estimation and global bifurcation analysis, Bull. Math. Biol., 56 (1994), 295-321. |
[24] |
A. M. Liapunov, "Probléme géné ral de la stabilité du Mouvement," Princeton University Press, Ann. of Math. Stud, 1947. |
[25] |
I. G. Malkin, "Theory of Stability of Motion," Translated by Atomic Energy Commission, 1952, 92-94. |
[26] |
J. J Patard, F. Saint, F. Velotti, C. C. Abbou and D. K. Chopin, Immune response following intravesical bacillus Calmette-Guerin instillations in superficial bladder cancer: A review, Urol. Res., 26 (1998), 155-159.doi: 10.1007/s002400050039. |
[27] |
V. A Pliss, The reduction principle in the theory of the stability motion, Izv.Akad. Nauk SSSR, Ser. Mat. 28 (1964), 1297-1324. |
[28] | |
[29] |
E. Shochat, D. Hart and Z. Agur, Using computer simulations for evaluating the efficacy of breast cancer chemotherapy protocols, Math. Models&Methods in Applied Sciences, 9 (1999), 599-615.doi: 10.1142/S0218202599000312. |
[30] |
K. R. Swanson, C. Bridge, J. D. Murray and E. C. Alvord, Virtual and real brain tumors: Using mathematical modeling to quantify glioma growth and invasion, J. Neurol. Sci., 216 (2003), 1-10.doi: 10.1016/j.jns.2003.06.001. |
[31] |
J. Wigginton and D. Kirschner, A model to predict cell-mediated immune regulatory mechanisms during human infection with Mycobacterium tuberculosis, J. Immunol., 166 (2001), 1951-1967. |
[32] |
Q. S. Zhang, A. Y. T. Leung and J. E. Cooper, Computation of normal forms for higher dimensional semi-simple systems, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis, 8 (2001), 559-574. |