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Lie algebra on synchronization of different systems: a generalized function for Hodgkin-Huxley neurons

Juan Gonzalo Barajas Ramirez, Ricardo Femat, Gualberto Solis-Perales
In this contribution two results are taken: (1) The synchronization of noiseless Hodgkin-
Huxley (HH) neurons is possible from robust feedback based on Lie algebra approaches and (2) the
fact that, from Lie algebra of vector fields, the generalized synchronization of different (triangular form)
chaotic systems can be used to derive an explicit synchronization function. Both results are extended to
derive the synchronization function in HH neurons despite this systems are not in triangular form. Thus,
the Lie algebra of vectors fields permits to establish a theoretical framework for finding the synchroniza-
tion function in chaotic systems in face they have different model.
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