Stability And Bifurcation Analysis In A Kind Of Model Of Economic Dynamics System

Following the rapid economic development,‘globalization’ is becoming the mostpopular subject throughout the world. However, in the trend of globalization, only byfollowing the law of economic development can economic development be achieved.Therefore, it is quite necessary to study the nature of economics system by usingmethods from dynamical system.In this paper, we mainly study a model of economic dynamics system, which iscalled the Kaldorian open economy macro dynamic model with money proposed earlierat a fixed exchange rate. We take adjustment speed of the goods marketα and degree ofcapital mobility β as parameters, and study the effects on the stability and bifurcation ofequilibrium of the dynamic system, by changing those parameter values.First, it is obtained that the system only has one equilibrium point, which is apositive one, and the expression of the equilibrium is also given. Second, the stabilityregion in the given parameter space is determined by employing the method ofcharacteristic equations. Next, we consider the stability and bifurcation of equilibriumin two scenarios, a) β change with α fixed, b) α change with β fixed. Then, therange of fixed parameter that enable the equilibrium to stay stable as well as experiencethe Hopf bifurcation, and the bifurcation value are all given. Finally, numericalsimulation is adopted to verify the given conclusions, and make some furthersupplements.