Sudden transition from equilibrium stability to chaotic dynamics in a cautious t?tonnement model

International Workshop on Nonlinear Maps and Applications 2015

Foroni, I.^1 ; Avellone, A.^1 ; Panchuk, A.^2

Department of Statistica e Metodi Quantitativi, University of Milano-Bicocca, Italy^1

Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivska str., Kyiv

01601, Ukraine^2

关键词: Asymptotic behaviors;    Border collision bifurcation;    Chaotic behaviors;    Chaotic dynamics;    Equilibrium stability;    Piecewise-smooth map;    Price adjustment;    Pure exchanges;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/692/1/012005/pdf
DOI  :  10.1088/1742-6596/692/1/012005

来源: IOP

【 摘 要 】

Discrete time price adjustment processes may fail to converge and may exhibit periodic or even chaotic behavior. To avoid large price changes, a version of the discrete time tâtonnement process for reaching an equilibrium in a pure exchange economy based on a cautious updating of the prices has been proposed two decades ago. This modification leads to a one dimensional bimodal piecewise smooth map, for which we show analytically that degenerate bifurcations and border collision bifurcations play a fundamental role for the asymptotic behavior of the model.