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. 2014 Aug 14;10(8):e1003783. doi: 10.1371/journal.pcbi.1003783

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© 2014 Cao et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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A: simulated stochastic (upper panel) or deterministic (lower panel) oscillations at . B: a typical stochastic solution projected on the plane. The average represents the average value of over the 20 . Statistics () of the initiation point (blue square), the peak (red square) and termination point (green square) are shown in the inset. 116 samples are obtained by applying a low threshold of and a high threshold of to . C: a typical periodic solution of the deterministic model (black curve), plotted in the phase space. The arrow indicates the direction of movement. is the slowest variable so that its variation during an oscillation is very small. This allows to treat as a constant ( in this case) and study the dynamics of the model in the phase space. The color surface is the surface where (called the critical manifold). The white N-shaped curve is the intersection of the critical manifold and the surface . D: projection of the periodic solution to the plane. The red N-shaped curve is the projection to the plane of the white curve shown in C. The evolution of the deterministic solution exhibits three different time scales separated by green circles (labelled by a, b and c) and indicated by arrows (triple arrow: fastest; double arrow: intermediate; single arrow: slowest).

Inline graphic — A: simulated stochastic (upper panel) or deterministic (lower panel) oscillations at . B: a typical stochastic solution projected on the plane. The average represents the average value of over the 20 . Statistics () of the initiation point (blue square), the peak (red square) and termination point (green square) are shown in the inset. 116 samples are obtained by applying a low threshold of and a high threshold of to . C: a typical periodic solution of the deterministic model (black curve), plotted in the phase space. The arrow indicates the direction of movement. is the slowest variable so that its variation during an oscillation is very small. This allows to treat as a constant ( in this case) and study the dynamics of the model in the phase space. The color surface is the surface where (called the critical manifold). The white N-shaped curve is the intersection of the critical manifold and the surface . D: projection of the periodic solution to the plane. The red N-shaped curve is the projection to the plane of the white curve shown in C. The evolution of the deterministic solution exhibits three different time scales separated by green circles (labelled by a, b and c) and indicated by arrows (triple arrow: fastest; double arrow: intermediate; single arrow: slowest).