He was a recipient of an International Security Studies grant provided by the Carnegie Corporation of New York, working in affiliation with the Program on the Analysis and Resolution of Conflicts, Maxwell School of Citizenship and Public Affairs, Syracuse University (1995).
During the 1997-1998 academic year, he was a Visiting Senior Fulbright Scholar, affiliated with the Center for Russian and East European Studies, Stanford University, US.
Ayvazyan worked as adjunct assistant professor of political science at the American University of Armenia, a Fellow at the American University of Armenia's Center for Policy Analysis, guest lecturer at the Yerevan State University and professor of political science of the Armenian State Academy of Governance.
He was team leader of the European Commission's sponsored Campaign Against "Corruption-Friendly" Legal and Social Settings in Armenia program in 2004-2005.
After the presidential elections in 2013, he wrote a highly critical article in the Harvard International Review, where he qualified the Russian-Western geopolitical game over the influence in Armenia as a lose-lose situation, which damages both their long-term strategic interests and the viability of Armenia.