and immune response, vol 11. Springer Sci-
ence & Business Media, New York- Pantel K, Alix-Panabie ́res C, Riethdorf S
(2009) Cancer micrometastasis. Nat Rev
Clin Oncol 6(6):339–351 - Hielscher A, Wirtz D (2013) A physical
sciences network characterization of
non-tumorigenic and metastatic cells. Sci
Rep 3:1449 - Bubendorf L (2000) Metastatic patterns of
prostate cancer: an autopsy study of 1,589
patients. Hum Pathol 31(5):578–583 - Prigogine I, Lefever R (1980) Stability pro-
blems in cancer growth and nucleation. Comp
Biochem Physiol 67B:389–393 - Delsanto PP, Romano A, Scalerandi M, Pes-
carmona GP (2000) Analysis of a “phase tran-
sition” from tumor growth to latency. Phys
Rev E 62:2547–2549 - Sole ́RV (2003) Phase transitions in unstable
cancer cell populations. Eur Phys J
35:117–124 - Davies PC, Demetrius L, Tuszynski JA (2011)
Cancer as a dynamical phase transition. Theor
Biol Med Model 8:30 - Strogatz SH (2000) Nonlinear dynamics and
chaos. Westview, Cambridge - Kuznetsov VA, Makalkin IA, Taylor MA, Per-
elson AS (1994) Nonlinear dynamics of
immunogenic tumors: parameter estimation
and global bifurcation analysis. Bull Math
Biol 56(2):295–321 - Llanos-Pe ́rez J, Betancourt-Mar A, De
Miguel M, Izquierdo-Kulich E, Royuela-
Garcı ́a M, Tejera E, Nieto-Villar J Phase tran-
sitions in tumor growth: II Prostate cancer
cell lines. Physica A 426:88–92 - Izquierdo-Kulich E, Nieto-Villar JM (2007)
Mesoscopic model for tumor growth. Math
Biosci Eng 4(4):687–698 - Anishchenko VS, Vadivasova TE, Okrokverts-
khov GA, Strelkova GI (2003) Correlation
analysis of dynamical chaos. Physica A 325
(1):199–212 - Kuznetsov YA (2013) Elements of applied
bifurcation theory, vol 112. Springer Science
& Business Media, Dusseldorf, Germany - Wolf A, Swift JB, Swinney HL, Vastano JA
(1985) Determining Lyapunov exponents
from a time series. Physica D 16(3):285–317 - Ziv J, Lempel A (1977) A universal algorithm
for sequential data compression. IEEE Trans
Inform Theory 23(3):337–343 - Ziv J, Lempel A (1978) Compression of indi-
vidual sequences via variable-rate coding.
IEEE Trans Inform Theory 24(5):530–536
56. Frederickson P, Kaplan JL, Yorke ED, Yorke
JA (1983) The Lyapunov dimension of
strange attractors. J Differ Equ 49
(2):185–207
57. Gear CW (1968) The automatic integration
of stiff ordinary differential equations. In:
Proceedings IFIP68. North-Holland,
Amsterdam, pp 187–193
58. Hegger R, Kantz H, Schreiber T (1999) Prac-
tical implementation of nonlinear time series
methods: the TISEAN package. Chaos 9
(2):413–435
59. Shilnikov AL, Turaev DV, Chua LO (2001)
Methods of qualitative theory in nonlinear
dynamics, vol 5. World Scientific, Singapore
60. Itik M, Banks SP (2010) Chaos in a three-
dimensional cancer model. Int J Bifurcat
Chaos 20(01):71–79
61. El-Gohary A (2008) Chaos and optimal con-
trol of cancer self-remission and tumor system
steady states. Chaos Solitons Fractals 37
(5):1305–1316
62. Mackey MC, Glass L (1977) Oscillation and
chaos in physiological control systems. Sci-
ence 197(4300):287–289
63. Posadas E, Criley S, Coffey D (1996) Chaotic
oscillations in cultured cells: rat prostate can-
cer. Cancer Res 56(16):3682–3688
64. Wolfrom C, Chau NP, Maigne ́J, Lambert JC,
Ducot B, Guerroui S, Deschatrette J (2000)
Evidence for deterministic chaos in aperiodic
oscillations of proliferative activity in long-
term cultured Fao hepatoma cells. Cell Sci
113(6):1069–1074
65. Sedivy R, Windischberger C, Svozil K,
Moser E, Breitenecker G (1999) Fractal anal-
ysis: an objective method for identifying atyp-
ical nuclei in dysplastic lesions of the cervix
uteri. Gynecol Oncol 75(1):78–83
66. Landini G, Rippin JW (1993) Fractal dimen-
sions of the epithelial-connective tissue inter-
faces in premalignant and malignant epithelial
lesions of the floor of the mouth. Anal Quant
Cytol Histol 15(2):144–149
67. Kitano H (2003) Cancer robustness: tumour
tactics. Nature 426:125
68. Betancourt-Mar JA, Nieto-Villar JM (2007)
Theoretical models for chronotherapy: peri-
odic perturbations in funnel chaos type.
Math Biosci Eng 4(2):177–186
69. Wells A (2006) Cell motility in cancer inva-
sion and metastasis, vol 8. Springer Science &
Business Media, New York
70. Volkenstein MV (2009) Entropy and infor-
mation, vol 57. Springer Science, New York
166 Sheyla Montero et al.