Abstract
A dynamical system is one whose state may be represented as a point in a space, where each point is assigned a vector specifying the evolution. The basic ideas of the mathematical theory of dynamical systems are presented here visually, with a minimum of discussion, using examples in low dimensions. The “AB portrait” is introduced as a record of attractors and basins. The basic dynamical bifurcations also are given, including examples of bifurcations with two controls. Extensions of dynamical concepts are proposed in order to allow modeling of hierarchical and complex systems. These extensions include serial and parallel coupling of dynamical systems in networks.
The references for the ideas in this chapter can be found in Chapter 30. —The Editor
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© 1987 Plenum Press, New York
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Abraham, R.H., Shaw, C.D. (1987). Dynamics. In: Yates, F.E., Garfinkel, A., Walter, D.O., Yates, G.B. (eds) Self-Organizing Systems. Life Science Monographs. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0883-6_30
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DOI: https://doi.org/10.1007/978-1-4613-0883-6_30
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