Figure - PMC

Skip to main content

View full-text article in PMC

. Author manuscript; available in PMC: 2016 Jun 21.

Published in final edited form as: J Theor Biol. 2014 May 14;375:77–87. doi: 10.1016/j.jtbi.2014.05.003

Fig. 6 — Bifurcation diagrams of ₃, described by Eq. (11), with respect to β, the slowly varying variable in the presence of uniform (A) and nonuniform (B) inter-clonal competitions. To generate nonuniform competition in (B), the following values for the competition scaling factors are used: ε₁₂ = 3, ε₁₃ = 1.1 and ε₃₃ = 0.782. Solid-(dashed-) black lines in panels (A) and (B) represent stable (unstable) steady states and gray-solid lines in panel (B) represent the branches of stable periodic orbits emerging from supercritical Hopf bifurcation points (HB1, HB2, HB3 and HB4). The two panels are truncated at β = 0.45 to magnify the bifurcation diagrams for small β, and because higher values of β do not alter the stable steady state ₃ = 0. As indicated, nonuniform competition induces oscillations in ₃.

Inline graphic — Bifurcation diagrams of ₃, described by Eq. (11), with respect to β, the slowly varying variable in the presence of uniform (A) and nonuniform (B) inter-clonal competitions. To generate nonuniform competition in (B), the following values for the competition scaling factors are used: ε₁₂ = 3, ε₁₃ = 1.1 and ε₃₃ = 0.782. Solid-(dashed-) black lines in panels (A) and (B) represent stable (unstable) steady states and gray-solid lines in panel (B) represent the branches of stable periodic orbits emerging from supercritical Hopf bifurcation points (HB1, HB2, HB3 and HB4). The two panels are truncated at β = 0.45 to magnify the bifurcation diagrams for small β, and because higher values of β do not alter the stable steady state ₃ = 0. As indicated, nonuniform competition induces oscillations in ₃.