Details

Autor(en) / Beteiligte

• Zhang, Wei-Bin,

Titel

Discrete dynamical systems, bifurcations and chaos in economics

Auflage

1st ed

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references (p. 427-437) and index.
• Cover; Contents; Preface; Difference equations in economics; Difference equations and economic analysis; Overview; Scalar linear difference equations; Linear first-order difference equations; Some concepts; Stabilities; Stabilities of nonhyperbolic equilibrium points; On dissipative maps; Linear difference equations of higher order; Equations with constant coefficients; Limiting behavior; One-dimensional dynamical economic systems; A model of inflation and unemployment; The one-sector growth (OSG model); The general OSG model; The overlapping-generations (OLG) model
• Persistence of inequality and developmentGrowth with creative destruction; Economic evolution with human capital; Urbanization with human capital externalities; The OSG model with money; The OSG model with labor supply; Time-dependent solutions of scalar systems; Periodic orbits; Economic bifurcations and chaos; Period-doubling bifurcations; Aperiodic orbits; Some types of bifurcations; Liapunov numbers; Chaos; Business cycles with knowledge spillovers; A cobweb model with adaptive adjustment; Inventory model with rational expectations; Economic growth with pollution
• The Solow and Schumpeter growth oscillationsMoney, growth and fluctuations; Population and economic growth; Higher dimensional difference equations; Phase space analysis of planar linear systems; Autonomous linear difference equations; Nonautonomous linear difference equations; Stabilities; Liapunov's direct method; Linearization of difference equations; Conjugacy and center manifolds; The Henon map and bifurcations; The Neimark-Sacker (Hopf) bifurcations; The Liapunov numbers and chaos; Higher dimensional economic dynamics; An exchange rate model; A two-sector OLG model
• Growth with government spendingGrowth with fertility and old age support; Growth with different types of economies; Unemployment, inflation and chaos; Business cycles with money and capital; The OSG model with heterogeneous households; Path-dependent evolution with education; Appendix; Proving proposition 7.81; Proving proposition 7.9.1; Epilogue; Appendix; Matrix theory; Systems of linear equations; Metric spaces; The implicit function theorem; The Taylor expansion and linearization; Concave and quasiconcave functions; Unconstrained maximization; Constrained maximization
• Dynamical optimizationBibliography; Index
• This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models
• English