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. Author manuscript; available in PMC: 2020 Feb 7.
Published in final edited form as: J Theor Biol. 2018 Nov 28;462:514–527. doi: 10.1016/j.jtbi.2018.11.034

Figure 2.

Figure 2.

Phase-plane portraits of piece-wise linear (PWL) and smooth, nonlinear (soft-H) ODE models of motifs discussed in the text. (A) PWL model of Motif 1A(i)-Case A, with γ1 = γ2. (B) PWL model of Motif 1A(i)-Case C, with γ2 = 2γ1. (C) Soft-H model of Motif 1A(i)-Case A, with γ1 = γ2. (D) Soft-H model of Motif 1A(i)-Case C, with γ2 = 2γ1. Parameter values are given in Table 3. In all four panels, the black lines are ‘trajectories’ starting from a variety of initial locations in state space and proceeding to one or the other of two stable steady states, at C1=1, C2=0 or at C1=0, C2=1. In cases C and D, the red curve is the C1-nullcline (where dC1/dt = 0) and the green curve is the C2-nullcline (where dC2/dt = 0). The red and green curves intersect at the third steady state, an unstable saddle point, in the interior of the unit square. The curve passing through the saddle point (yellow in panel C) separates the ‘domains of attraction’ of the two stable steady states.