Cygnus X-3 binary system is a famous object studied over the wide range of electromagnetic spectrum. Early detections of ultra-high energy gamma-rays from Cygnus X-3 by Kiel, Havera Park and then by Akeno triggered the construction of several large air shower detectors. Also, Cygnus X-3 has been proposed to be one of the most powerful sources of charged cosmic ray particles in the Galaxy. The results of twenty-year observations of the Cyg X-3 binary at energies 800 GeV - 85 TeV are presented with images, spectra during periods of flaring activity and at low flux periods. The correlation of TeV flux increases with flaring activity at the lower energy range of X-ray and radio emission from the relativistic jets of Cygnus X-3 is found as well as 4.8-hour orbital modulation of TeV γ-ray intensity. Detected modulation of TeV γ-ray emission with orbit and important characteristics of Cyg X-3 such as the high luminosity of the companion star and the close orbit leads to an efficient generation of γ-ray emission through inverse Compton scattering in this object. The different type variability of very high-energy γ-emission and correlation of radiation activity in the wide energy range can provide essential information on the mechanism of particle production up to very high energies.
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