Dynamical Systems An Introduction with Applications in Economics and Biology
The favourable reception of the first edition and the encouragement received from many readers have prompted the author to bring out this new edition. This provides the opportunity for correcting a number of errors, typographical and others, contained in the first edition and making further improvem...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1994, 1994
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| Edition: | 2nd ed. 1994 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 8.2 The Gradient Dynamic Systems (GDS)
- 8.3 Lagrangean and Hamiltonian Systems
- 8.4 Hamiltonian Dynamics
- 8.5 Economic Applications
- 8.6 Conclusion
- 9 Simplifying Dynamical Systems
- 9.1 Introduction
- 9.2 Poincaré Map
- 9.3 Floquet Theory
- 9.4 Centre Manifold Theorem (CMT)
- 9.5 Normal Forms
- 9.6 Elimination of Passive Coordinates
- 9.7 Liapunov-Schmidt Reduction
- 9.8 Economic Applications and Conclusions
- 10 Bifurcation, Chaos and Catastrophes in Dynamical Systems
- 10.1 Introduction
- 10.2 Bifurcation Theory (BT)
- 10.3 Chaotic or Complex Dynamical Systems (DS)
- 10.4 Catastrophe Theory (C.T.)
- 10.5 Concluding Remarks
- 11 Optimal Dynamical Systems
- 11.1 Introduction
- 11.2 Pontryagin’s Maximum Principle
- 11.3 Stabilization Control Models
- 11.4 Some Economic Applications
- 11.5 Asymptotic Stability of Optimal Dynamical Systems (ODS)
- 11.6 Structural Stability of Optimal Dynamical Systems
- 11.7 Conclusion
- 1 Introduction
- 2 Review of Ordinary Differential Equations
- 2.1 First Order Linear Differential Equations
- 2.2 Second and Higher Order Linear Differential Equations
- 2.3 Higher Order Linear Differential Equations with Constant Coefficients
- 2.6 Conclusion
- 3 Review of Difference Equations
- 3.1 Introduction
- 3.2 First Order Difference Equations
- 3.3 Second Order Linear Difference Equations
- 3.4 Higher Order Difference Equations
- 3.5 Stability Conditions
- 3.6 Economic Applications
- 3.7 Concluding Remarks
- 4 Review of Some Linear Algebra
- 4.1 Vector and Vector Spaces
- 4.2 Matrices
- 4.3 Determinant Functions
- 4.4 Matrix Inversion and Applications
- 4.5 Eigenvalues and Eigenvectors
- 4.6 Quadratic Forms
- 4.7 Diagonalization of Matrices
- 4.8 Jordan Canonical Form
- 4.9 Idempotent Matrices and Projection
- 4.10 Conclusion
- 5 First Order Differential Equations Systems
- 5.1 Introduction
- 5.2 Constant Coefficient Linear Differential Equation (ODE) Systems
- 5.3 Jordan Canonical Form of ODE Systems
- 5.4 Alternative Methods for Solving ? = Ax
- 5.5 Reduction to First Order of ODE Systems
- 5.6 Fundamental Matrix
- 5.7 Stability Conditions of ODE Systems
- 5.8 Qualitative Solution: Phase Portrait Diagrams
- 5.9 Some Economic Applications
- 6 First Order Difference Equations Systems
- 6.1 First Order Linear Systems
- 6.2 Jordan Canonical Form
- 6.3 Reduction to First Order Systems
- 6.4 Stability Conditions
- 6.5 Qualitative Solutions: Phase Diagrams
- 6.6 Some Economic Applications
- 7 Nonlinear Systems
- 7.1 Introduction
- 7.2 Linearization Theory
- 7.3 Qualitative Solution: Phase Diagrams
- 7.4 Limit Cycles
- 7.5 The Liénard-Van der Pol Equations and the Uniqueness of Limit Cycles
- 7.6 Linear and Nonlinear Maps
- 7.7 Stability of Dynamical Systems.-7.8 Conclusion
- 8 Gradient Systems, Lagrangean and Hamiltonian Systems
- 8.1 Introduction
- 12 Some Applications in Economics and Biology
- 12.1 Introduction
- 12.2 Economic Applications of Dynamical Systems
- 2.1. Flexible Multiplier-Accelerator Models
- 2.2. Kaldor’s Type of Flexible Accelerator Models
- 2.3. Goodwin’s Class Struggle Model
- 2.1. Two Sector Models
- 2.2. Economic Growth with Money
- 2.3. Optimal Economic Growth Models
- 2.4. Endogenous Economic Growth Models
- 12.3 Dynamical Systems in Biology
- 12.4 Bioeconomics and Natural Resources
- 12.5 Conclusion