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Fig. 5 | Biology Direct

Fig. 5

From: Onset, timing, and exposure therapy of stress disorders: mechanistic insight from a mathematical model of oscillating neuroendocrine dynamics

Fig. 5

Slow and fast nullclines and overall flow field. a The nullcline of c s in the ε→0 limit is defined by c s=〈c (c)〉. To plot these slow nullclines together with the fast c-nullclines, we transform the variable c s and represent it by q through the relation q=q 0 h(c s). These transformed nullclines then become a function of c and can be plotted together with the fast c-nullclines. For each fixed value of c, o(t;c) is computed by employing a built-in DDE solver dde23 in MATLAB. The numerical solution is then used to approximate 〈c (c)〉 in Eq. 25 by Euler’s method. The q-nullcline shifts to the right and gets steeper as k increases. b The fast c-nullcline defined by q g c (c)=q 2 c (black curve) is plotted together with the slow c s-nullcline plotted in the (q,c) plane (“q-nullcline,” blue curve). Here, two intersections arise corresponding to a high-cortisol normal (N) stable state and a low-cortisol diseased (D) stable state. The flow vector field is predominantly aligned with the fast directions toward the c-nullcline

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