This book was first pUblished in 1989 as volume 336 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and it reappeared in a 2nd edition as a Springer monograph in 1991. After considerable revisions it appeared in a 3rd edition in 1993. The origin, still visible in the 3rd edition, was the joint work of the author with Professor Martin J. Beckmann, documented in two co-authored mono graphs "Spatial Economics" (North-Holland 1985), and "Spatial Structures" (Springer-Verlag 1990). Essential dynamics had, however, been almost com pletely lacking in these works, and the urge to focus the dynamic issues was great. To fill this particular gap was the aim of the previous editions, and so the spatial aspect provided core and focus. In the present edition a substantial quantity of spatial issues have been removed: All those that were dynamic only in the sense that structures were characterized which were structurally stable, or robust in a changing world. The removed material has meanwhile been published as a separate mono graph under the title "Mathematical Location and Land Use Theory" (Springer-Verlag 1996).
Auflage
4th completely rev. and enlarged ed.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Editions-Typ
Illustrationen
1
1 s/w Tabelle
119 figures, 1 table
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Gewicht
ISBN-13
978-3-540-62768-5 (9783540627685)
DOI
10.1007/978-3-642-60775-2
Schweitzer Klassifikation
1 Introduction.- 1.1 Dynamics Versus Equilibrium Analysis.- 1.2 Linear Versus Nonlinear Modelling.- 1.3 Perturbation Methods.- 1.4 Structural Stability.- 1.5 Chaos and Fractals.- 1.6 The Choice of Topics Included.- 2 Differential Equations.- 2.1 The Phase Portrait.- 2.2 Linear Systems.- 2.3 Structural Stability.- 2.4 Limit Cycles.- 2.5 The Hopf Bifurcation.- 2.5 The Saddle-Node Bifurcation.- 2.7 Perturbation Methods: Poincaré-Lindstedt.- 2.8 Perturbation Methods: Two-Timing.- 2.9 Forced Oscillators: van der Pol.- 2.10 Forced Oscillators: Duffing.- 2.11 Chaos.- 2.12 A Short History of Chaos.- 3 Iterated Maps.- 3.1 Introduction.- 3.2 The Logistic Map.- 3.3 The Lyapunov Exponent.- 3.4 Symbolic Dynamics.- 3.5 Sarkovskii's Theorem and the Schwarzian Derivative.- 3.6 The Hénon Model.- 3.7 Lyapunov Exponents in 2D.- 3.8 Fractals and Fractal Dimension.- 3.9 The Mandelbrot Set.- 4 Monopoly.- 4.1 Introduction.- 4.2 The Model.- 4.3 Adaptive Search.- 4.4 Numerical Results.- 4.5 Fixed Points and Cycles.- 4.6 Chaos.- 4.7 A Case with Two Products.- 4.8 Discussion.- 5 Duopoly and Oligopoly.- 5.1 Introduction.- 5.2 The Cournot Model.- 5.3 Stackelberg Equilibria.- 5.4 The Iterative Process.- 5.5 Stability of the Cournot Point.- 5.6 Periodic Points and Chaos.- 5.7 Adaptive Expectations.- 5.8 Adjustments Including Stackelberg Points.- 5.9 Oligopoly with Three Firms.- 5.10 Stackelberg Action Reconsidered.- 5.11 The Iteration with Three Oligopolists.- 5.12 Back to "Duopoly".- 5.13 Changing the Order of Adjustment.- 6 Business Cycles: Continuous Time.- 6.1 The Multiplier-Accelerator Model.- 6.2 The Original Model.- 6.3 Nonlinear Investment Functions and Limit Cycles.- 6.4 Limit Cycles: Existence.- 6.5 Limit Cycles: Asymptotic Approximation.- 6.6 Limit Cycles: Transients and Stability.- 6.7 The Two-Region Model.- 6.8 The Persistence of Cycles.- 6.9 Perturbation Analysis of the Coupled Model.- 6.10 The Unstable Zero Equilibrium.- 6.11 Other Fixed Points.- 6.12 Properties of Fixed Points.- 6.13 The Arbitrary Phase Angle.- 6.14 Stability of the Coupled Oscillators.- 6.15 The Forced Oscillator.- 6.16 The World Market.- 6.17 The Small Open Economy.- 6.18 Stability of the Forced Oscillator.- 6.19 Catastrophe.- 6.20 Period Doubling and Chaos.- 6.21 Relaxation Cycles.- 6.22 Relaxation: The Autonomous Case.- 6.23 Relaxation: The Forced Case.- 6.24 Three Identical Regions.- 6.25 On the Existence of Periodic Solutions.- 6.26 Stability of Three Oscillators.- 6.27 Simulations.- 7 Business Cycles: Continuous Space.- 7.1 Introduction.- 7.2 Interregional Trade.- 7.3 The Linear Model.- 7.4 Coordinate Separation.- 7.5 The Square Region.- 7.6 The Circular Region.- 7.7 The Spherical Region.- 7.8 The Nonlinear Spatial Model.- 7.9 Dispersive Waves.- 7.10 Standing Waves.- 8 Business Cycles: Discrete Time.- 8.1 Introduction.- 8.2 Investments.- 8.3 Consumption.- 8.4 The Cubic Iterative Map.- 8.5 Fixed Points, Cycles, and Chaos.- 8.6 Formal Analysis of Chaotic Dynamics.- 8.7 Coordinate Transformation.- 8.8 The Three Requisites of Chaos.- 8.9 Symbolic Dynamics.- 8.10 Brownian Random Walk.- 8.11 Digression on Order and Disorder.- 8.12 The General Model.- 8.13 Relaxation Cycles.- 8.14 The Slow Feed Back.- 8.15 The Autonomous Term: Changes of Fixed Points.- 8.16 The Autonomous Term: Response of the Chaotic Process.- 8.17 Lyapunov Exponents and Fractal Dimensions.- 8.18 Non-Relaxation Cycles.- 8.19 Conclusion.- References.
