Pomeau-Manneville intermittency

In their study of CMLs exhibiting a Pomeau-Manneville intermittency, Crutchfield and Kaneko [crutch87] have observed the following general behavior ... 

We should contrast the so-called Pomeau-Manneville intermittency [pomeauSO] with intermittency via pattern competition [kaneko87]. We have commented earlier... 

Y. Pomeau and P. Manneville Intermittent transition to turbulence in dissipative dynamical systems. Comm. Math. Phys. 1980, 74 189-197. 

In a separate article [10] we considered a modified version of a onedimensional intermittent chaotic system, the Manneville-Pomeau map [18]. We numerically confirmed the fractional power scaling of excess heat production. 

We should not be surprised to see ghosts—they always occur near saddle-node bifurcations (Sections 4.3 and 8.1) and indeed, a tangent bifurcation is just a saddle-node bifurcation by another name. But the new wrinkle is that the orbit returns to the ghostly 3-cycle repeatedly, with intermittent bouts of chaos between visits. Accordingly, this phenomenon is known as intermittency (Pomeau and Manneville 1980). 

Intermittency is not just a curiosity of the logistic map. It arises commonly in systems where the transition from periodic to chaotic behavior takes place by a saddle-node bifurcation of cycles. For instance. Exercise 10.4.8 shows that intermittency can occur in the Lorenz equations. (In fact, it was discovered there see Pomeau and Manneville 1980). 

Pomeau, Y., and Manneville, P. (1980) Intermittent transition to turbulence in dissipa-... 

Manneville-Pomeau Intermittent transition Chemical reaction Benard experiment... 

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