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Figure 10 | Theoretical Biology and Medical Modelling

Figure 10

From: Mathematical modeling of solid cancer growth with angiogenesis

Figure 10

Bifurcation diagram varying γ. The bifurcation diagram of T ̄ varying γ, showing the attracting regions. In (a) we show wide range of variation of γ, and in (b), a zoom near origin. For γ <γth(b) the trivial Q ̄ 0 is attractor for all initial conditions (region Ic). For γ > γth(a), with respect to the coordinates of small equilibrium point Q ̄ < * , the trivial Q ̄ 0 is attractor for regions I, Ia and Ib; and we have three possibilities: (1) for γ t h <γ< γ 1 c , the non-trivial Q ̄ > * is attractor for initial conditions in regions II and III; (2) for γ 1 c <γ< γ 2 c , stable limit cycle circulating unstable Q ̄ > * , in regions IIa and IIIa; and (3) for γ> γ 2 c , trivial Q ̄ 0 is attractor for regions IV and V. In the latter case, the way to reaching the trivial equilibrium is different for initial conditions in Ib and IV or V. The scales of vertical and horizontal axes must be multiplied by the factors shown in the legends to obtain the actual values.

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