The topic of growth rate differentials between countries has been a main theme in my work from the very beginning. It was the main topic of my PhD thesis of 1992. Chapter 6 of that thesis contains my model of catching up and falling behind (see picture below), which was also published in 1991 in the Elsevier Journal Structural Change and Economic Dynamics. if you do not have access to that journal, you can download the paper here.
Four years later, in 1995, I published an overview piece on convergence and divergence (entitled "Convergence in the Global Economy. A Broad Historical Viewpoint") in the same journal, direct download is here.
When I teamed up with Jan Fagerberg in the 1990s, we started working on convergence at the regional level. We published a paper in Journal of Common Market Studies in 1996 on convergence in Europe (direct download here), and the next year one together with Marjolein Caniëls in Regional Studies (direct download here). Marjolein did her PhD on this topic, and together we published an evolutionary model of regional growth rate differentials in Journal of Evolutionary Economics in 2001 (direct download here). In 2003, Jan and I (and co-authors) extended the regional convergence work to include an evaluation of the EU Structural Funds (direct download here).
With Jan, I also continued working at the global level, leading to a paper that included more recent global convergence trends and which was published in Research Policy in 2002 (direct download), and one in International Journal of Technological Learning, Innovation and Development in 2007. With Eddy Szirmai, I looked at the role of the manufacturing sector in growth rate differentials, leading to a published paper in 2015 (direct download).