This paper reports the dynamical analysis of the business cycles of 12 (developed and developing) countries over the last 56 years by applying computational techniques used for tackling complex systems. They reveal long-term convergence and country-level interconnections because of close contagion effects caused by bilateral networking exposure. Interconnectivity determines the magnitude of cross-border impacts. Local features and shock propagation complexity also may be true engines for local configuration of cycles. The algorithmic modeling proves to represent a solid approach to study the complex dynamics involved in the world economies.