Nonlinear Keynesian　Dynamics and Chaos

概要

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It is my purpose to examine a stability/instability of the nonlinear Keynesian Dynamics mathematically, consequently whether that model would include chaos or not. The development of our discussion is made as follows : (1) Nonlinear Keynesian Dynamics can be shown with a second order differential equation --- that is, Liénard’s differential equation --- in relation to a real national income Y. (2) The simplest case of Liénard’s differential equation is the Van der Pol differential equation. (3) The properties of solution and the limit cycle in relation to the Van der Pol differential equation. (4) If an exogenous oscillation could be given to the Van der Pol differential equation which is the Keynesian Dynamical Model, the synchronization phenomena would have occurred, as a result of it, whether the nonlinear dynamic system would arouse chaos or not. These issues are discussed
2009-03-15