Study of structures of singular phenomena via complex global analysis

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We have obtained the concrete formula of the monodromy of a certain confluent hypergeometric system which can be written in a Hamiltonian form. The method may be extended to more general system of equations and may be applied to the study of connection formulas near the irregular singular point. The method has some similarity to the so-called KAM theory.The other result of the research is the proof of the Borel summability of a singular perturbative formal solution of a certain a multi-dimensional Fuchsian equation. This results was proved in the case of one variable. Using the method in the above we have analyzed the analytic behavior of Lotoka Volterra system of three species with evolutional effect.