Stability analysis of some dynamic economic systems modeled by state-dependent delay differential equations

Abstract

The research subject of many studies is the asymptotical behavior of dynamic systems with both continuous and discrete time scales for economical approaches. The qualitative theory of differential or difference equations is the main basis of these studies. When modeling using ordinary differential equations, the delays in the system are always ignored. However, even a small amount of delay in the system can cause significant changes in the system. For this reason, it is more realistic to use delayed differential equations while modeling the majority of the problems encountered. Moreover, some research showed us that some delays in the systems vary with respect to the internal effects of the system. In this case, using of state-dependent delay differential equations is much more suitable. In this paper, Kaldorian macro dynamic model with Kaleckian investment delay and models of goods market with supply delay are investigated. First, the classical models are introduced, and then the effects of the delays in the system are discussed. Finally, general systems of state-dependent delay differential equations covering these models are analyzed.