The Elements of a Nonlinear Theory of Economic Dynamics [Paperback]

Elements of a Nonlinear Theory of Economic Dynamics provides both a framework and a survey of its needs. First, principle results and techniques of the theory relevant to applications in dynamic economics are discussed, then their application in view of older endogenous cycle theories are considered in a unified mathematical framework. Models incorporating the government budget constraint and the Goodwin model are analysed using the method of averaging and the centre manifold theory. The dynamic instability problem is solved by placing models in a nonlinear framework.Elements of a Nonlinear Theory of Economic Dynamics provides both a framework and a survey of its needs. First, principle results and techniques of the theory relevant to applications in dynamic economics are discussed, then their application in view of older endogenous cycle theories are considered in a unified mathematical framework. Models incorporating the government budget constraint and the Goodwin model are analysed using the method of averaging and the centre manifold theory. The dynamic instability problem is solved by placing models in a nonlinear framework.1. The Need for a Nonlinear Theory of Economic Dynamics.- 1.1 Introduction.- 1.2 Early Nonlinear Theories.- 1.3 Development of the Theory of Dynamical Systems.- 1.4 Problems in the Current State of Economic Dynamics.- 2. The Theory of Dynamical Systems.- 2.1 Introduction.- 2.2 Existence and Uniqueness Results.- 2.3 The Linear System x  Ax.- 2.4 Nonlinear Systems on the Plane.- 2.5 Analysis of Limit Cycles.- 2.6 Relaxation Oscillations.- 2.7 Higher Dimensional Nonlinear Systems.- Appendix 2.1.- 3. A New Look at Some old Endogenous Cycle Theories.- 3.1 Introduction.- 3.2 A General Model of Multiplier- Accelerator Interactions.- 3.3 Goodwins Nonlinear Accelerator Model.- 3.4 A Saturation Type Nonlinear Accelerator.- Appendix 3.1.- Appendix 3.2.- 4. Analysis of the Effects of Time Lags and Nonlinearities l|