Petri nets are used to extract information from the complex and negative eigenvalues of a von Neumann model employing the US sector-level use tables from 1997 to 2013. The complex eigenvalues show a cyclical component having a period of about 10 years. Sectors that contribute most to the cyclical component are agriculture, mining, retail trade, construction, and utilities. Negative eigenvalues indicate the instability in the economy from 1997 to 2009. In 2010 a Neimark-Sacker bifurcation boundary is crossed, beyond which the economy exhibits damping. The point of critical damping is approached in 2012. In 2013 the economy exhibits over-damping.

Keywords: Petri net, von Neumann growth model, Leontief model, eigenvalue, business cycle, use table, Neimark-Sacker bifurcation, over-damping

JEL classification: C65, C67, E32