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Original Articles

Association between competition and obligate mutualism in a chemostat

, , &
Pages 635-647 | Received 24 Nov 2008, Published online: 09 Oct 2009

Figures & data

Figure 1. Location of graph Γ1 with regard to the graph Γ2.

Figure 1. Location of graph Γ1 with regard to the graph Γ2.

Figure 2. β1=2.2, β2=2, α12=0.35, ω12=5.

Figure 2. β1=2.2, β2=2, α1=α2=0.35, ω1=ω2=5.

Figure 3. β1=2, β2=2.2, α1=0.195, α2=0.18, ω12=10.

Figure 3. β1=2, β2=2.2, α1=0.195, α2=0.18, ω1=ω2=10.

Figure 4. Γ1 and Γ2 are concave.

Figure 4. Γ1 and Γ2 are concave.

Figure 5. Left: the green trajectories are filling the domain R* of coexistence and converging to the equilibrium N. The red trajectories converge to (0, 0) and fill the domain R 0. The boundary of R 0 and R* consists in the two stable trajectories of the saddle point S. Right: the domain R 0 is the whole domain Ω. Available in colour online.

Figure 5. Left: the green trajectories are filling the domain R* of coexistence and converging to the equilibrium N. The red trajectories converge to (0, 0) and fill the domain R 0. The boundary of R 0 and R* consists in the two stable trajectories of the saddle point S. Right: the domain R 0 is the whole domain Ω. Available in colour online.

Figure 6. Left: the red trajectories fills the domain R 0. The blue, green and yellow trajectories are filling the coexistence domain R*. Blue trajectories converges to N 1, green ones to N 2 and yellow ones to N 3; the reached equilibrium depends on initial conditions. Right: the domain R 0 is the whole domain Ω. Available in colour online.

Figure 6. Left: the red trajectories fills the domain R 0. The blue, green and yellow trajectories are filling the coexistence domain R*. Blue trajectories converges to N 1, green ones to N 2 and yellow ones to N 3; the reached equilibrium depends on initial conditions. Right: the domain R 0 is the whole domain Ω. Available in colour online.

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