By Albert R. Baswell

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Ivancevic subcortical neural system performs both local and global (loco)motion control: first reflexly controlling contractions of individual muscles, and then orchestrating all the muscles into synergetic actions in order to produce efficient movements. While the local reflex control of individual muscles is performed on the spinal control level, the global integration of all the muscles into coordinated movements is performed within the cerebellum [28, 29]. All hierarchical subcortical neuro–muscular physiology, from the bottom level of a single muscle fiber, to the top level of cerebellar muscular synergy, acts as a temporal out|in reaction, in such a way that the higher level acts as a command/control space for the lower level, itself representing an abstract image of the lower one: 1.

Unfortunately, the utility of Rayleigh-Kuo condition is rather limited, since it does not give any information about the growing perturbations. Moreover, this necessary condition is satisfied in many cases, for example, for any wave (55) if n > 2 and wave amplitude fn0 is large enough. For a non-zonal RH wave, no instability condition analogeous to that by Rayleigh-Kuo has been developed. The instability conditions (64) and (68), instead of the structure of basic flow, refer to the structure of the growing perturbation and relate with the basic flow only by means of its degree n.

In this connection, the next problem of significant importance is to know if the RH wave is orbitally stable. Acknowledgments This work was supported by the PAPIIT grant IN105608 (UNAM, Mexico), projects 46265-A1 and FOSEMARNATd-2004-01-160 (CONACyT, Mexico), and SNI grant 14539 (CONACyT, Mexico). References [1] L. Rayleigh, On the stability or instability of certain fluid motions, Proc. London Math. Soc. 11 (1880), 57–70. Liapunov and Normal-Mode Instability of the Rossby-Haurwitz Wave 25 [2] R.

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