Fig 1.
Phase portrait in the original variables: a) Regime I for cd > 1 and f < d.
b) Regime II for cf < 1, cd < 1 and f < d. c) Regime III for cf > 1, cd > 1 and f > d. The separatrix in given in blue. d) Regime IV for cd < 1 and f > d.
Fig 2.
The potential function V(u): a) cd > 1, f < d and cf < 1.
b) cd > 1, f < d and cf > 1. c) cd < 1 and f < d. d) cd > 1 and f > d. e) cd < 1, f > d and cf > 1. f) cd < 1, f > d and cf < 1. The value of each parameter is the same used in Fig 1 for b), c), d) and f) subfigures. Subfigure a) was obtained with c = 1.65, d = 0.75 and f = 0.7. Subfigure e) was obtained with c = 1, d = 0.66 and f = 1.1.
Fig 3.
Effect of external stimulus with low continuous dose, in the original coordinates (19): a) Regime I.
b) Regime II. c) Regime III. The separatrix is given in blue. d) Regime IV.
Fig 4.
System on regime IV under a periodic perturbation, in original coordinates: a) limit cycle for ; b) solutions for
; c) limit cycle for
; d) solutions for
; e) non-chaotic attractor for
; f) solutions for
.
The parameters values are c = 1, d = 0.66, f = 1.1 and A1 = 0, which gives and A = 0.175.
Fig 5.
Both Lyapunov exponents as function of the steps n (leftt) and maximun Lyapunov exponent (right) as a function of n.
Fig 6.
Maximum (Max.) Lyapunov exponent as a function of each of the model parameters c (top left box), d (top right box), f (center left box), A (center right box) and (lower left and right boxes).
Fig 7.
Fitting of the evolution of the unperturbed Ehrlich tumor volume given by the Lotka-Volterra and Gompertz-MBBG models to experimental data.
Star points correspond to the experimental data, black line to the LV model and red line to the MBBG equation. Blue line corresponds to the evolution of the volume of healthy cells given by the LV model.
Fig 8.
Schematic representation of: a) magnetic bed (left subfigure) and b) cancer patient lying in nonmagnetic bed inside the magnetic system formed by a pair of coils (courtesy of Luis Bergues Cabrales) (right subfigure).