How linear growth in real GDP per capita rips the world up

I wrote a paper "Real GDP per capita: global redistribution of economic power" in 2020 (available on arxiv.org) explaining the increasing frequency and atrocity of collisions between developed and developing countries. This is the final paragraph. 

"Finally, in the world of the rapid growth of the future economic behemoths and stagnation of the most developed countries conflicts are inevitable. Unfair trade restrictions, political pressure, media attacks, propaganda, military aggression, and other dimensions of these conflicts may only rise in amplitude and extent. These conflicts involve new countries in the global clash, which also includes the clash of civilizations as an additional dimension. This is only because the growth in real GDP per capita is a linear function of time. In the exponential economic world, the lead of developed countries would be eternal as they had better start conditions and the exponent provides the increasing economic gap. In the linear economic world, the lead in GDPpc is constant, the chasing countries grow faster and the gap is shrinking in relative terms."