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Figure 3 | Biology Direct

Figure 3

From: Oscillatory dynamics in a model of vascular tumour growth - implications for chemotherapy

Figure 3

Partition of ( δ , d p )-space based on stability of wave trains. Figure showing where in (δ, d p )-space (as determined by (A-7) in the Appendix (additional file 1)) the wake behind the invading wave of tumour cells is stable (shaded region) and where it is unstable (white region). The stability analysis requires d s , where denotes the value of d s at which the Hopf bifurcation occurs; thus in our (δ, d p )-space we mark by solid lines contours where (as calculated from (A-11) in the Appendix (additional file 1)) is constant (corresponding values are labelled on the contours). For a case of stability ((δ, d p ) = (0.65, 0.6) and ds ≈ 0.2) tumour cell invasion into the spatially homogeneous vessel-only steady state results in regular spatio-temporal oscillations (see Figure 4), while in the case of instability ((δ, d p ) = (1.0, 0.6) and ds ≈ 0.2), irregular spatio-temporal oscillations develop (see Figure 5). Key: shaded region: wave stability; white region: wave instability; solid lines: lines where is constant. Parameter values: η0 = 0.5, s β = 0.4 and σ p = 0.

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