Abstract
In previous chapters, some fundamental concepts of algebra and differential geometry were presented. This chapter is devoted to an overview of dynamical systems that play a fundamental role in building mathematical models of reality.
Keywords
- Weierstrassian Analysis
- Linear Stability Properties
- α-Lipschitz Function
- Ordinary Differential Equations (ODEs)
- Higher-order ODEs
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Notes
- 1.
- 2.
This solution is obtainable at once by the method of variable separation. However, the reader can easily verify that it is really a solution for any C.
- 3.
For the application of differential equations to economy, see, for instance, [55].
- 4.
For a proof, see, for instance, [40].
- 5.
Readers will find in [35] many programs, written using Mathematica, that allow for the analysis of many stability problems.
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Romano, A. (2012). An Overview of Dynamical Systems. In: Classical Mechanics with Mathematica®. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8352-8_10
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