Arnold tongue

Slowly reduce the amplitude To give sufficient spissitude So that we can just pull him through The Arnold tongue at p by q. 

Fig. 7.2. FVoiit propagation reversal (n = 1,q = 0.5). (a) Standing kinks are found along the dashed line = 1.8) in the Arnold tongue, (b) Dependences of velocity V on spatial train period A for /3 = 1.8 (solid line) and B = 5.0 (dashed line) here v = 0.5525. B — 0.053. Space-tiiite diagrams showing behavior of wave patterns after termination of a jjacemaker in media with (c) B = 5.0 and (d) B = 1.8 the same other parameters as in part b, local values of Rerj(x, t) are shown in gray scale.

Note that, in the phase approximation, the boundaries of the Arnold tongue are B = Ba v)- The line B = is shown as the dashed line in Fig. 

As follows from (7.6), the condition for existence of stationary periodic trains is If (uj) < 0. Tliis means that they are found inside the region of the Arnold tongue, lying between the line B = and the (nearest)... 

Fig. 13.2. Family of syndirooization regions, or Arnold tongues (sdieinatically). The miinbers on top of each tongue indicate the order of locking e.g., 2 3 means that the relation =. 30 is fulfilled, (b) The O/oi vs. w plot for a fixed amplitude of the force (.shown by the dashed line in (a)) has a characteristic shape, known as the devtl s staircase, (hi this scheme the variation of the frec uency ratio between the main plateaus of the staircase is not sliowii),...

Note that both the saddles and nodes appearing inside the resonant wedge (called Arnold tongue, sometimes) lie on the invariant curve (stable if Li < 0 or unstable if L >0). Since the only stable invariant curve that can go through a saddle is its unstable manifold, and since the only unstable curve that can also go through a saddle is its stable manifold, it follows that inside the resonance zone the invariant curve is the union of the separatrices of saddles (imstable separatrices if Li < 0, or stable separatrices if L > 0) that terminate at the nodes. 

Burmeister JJ, Arnold MA, Small GW. Noninvasive blood glucose measurements by near infrared transmission spectroscopy across human tongues. Diabetes Technology Therapeutics 2000, 2, 5-16. 

An excellent and succinct overview is available in Kumaravel Rajakumar, Pellagra in the United States A Historical Perspective, Southern Medical Journal 93 (2000) 272-277. The identification of niacin as the specific pellagra-preventing factor was first reported in Conrad Arnold Elvehjem, The Isolation and Identification of the Anti-Black Tongue Factor, Journal of Biological Chemistry 123 (1938) 137-149. 

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