Fixed Points: Creation and Destruction
| Autor: | John Milton, Toru Ohira |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Mathematics as a Laboratory Tool ISBN: 9783030695781 Mathematics as a Laboratory Tool ISBN: 9781461490951 |
| DOI: | 10.1007/978-3-030-69579-8_5 |
| Popis: | The fixed point of a dynamical system describes a time-independent state. Depending on the nature of the interactions between a system and its surroundings, the fixed point can be either an equilibrium or a steady state. In the last chapter, we saw that the responses of the system following a perturbation away from the fixed point can be used to assess the stability of the fixed point, namely its resistance to change. Stability depends on the values of the parameters. This statement follows from the fact that the eigenvalues are determined by the parameters. This observation suggests another way to explore dynamical systems: we vary the parameters and observe how the dynamics change. There are two types of changes that we can expect to observe as parameters are changed. First, there can be changes in the stability of a fixed point: it may be stable for one range of parameter values and unstable for another range. Second, it is possible that as parameter values change, fixed points are created or destroyed. |
| Databáze: | OpenAIRE |
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