Abstract
In Chap. 2, we introduced linear system state equations. In this chapter, the discussion is extended to non-linear systems and their general dynamic properties. While Chap. 2 primarily adopted a numerical approach, here we focus on the deductive approach. In the latter half of the chapter, evolutionary games are introduced as a template for discussion.
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Notes
- 1.
The “linear” quality of a system is truly beneficial in engineering. No sharp fluctuations develop over time; therefore, future behavior is easily extrapolated from currently available information.
- 2.
Chikuma Scholastic Collection has published a three part Japanese edition of this seminal work (Ginbayashi et al.), reprint (2009).
- 3.
This is referred to as strategy adaptation.
- 4.
This is referred to as evolution.
- 5.
The proportion of cooperative members at the start of a series of games is 0.5.
- 6.
Strictly speaking PD satisfying D g = D r .
- 7.
This situation accords with common sense. If a game is played against the same partner each time rather than against an unknown one, both individuals should accept the cooperation option to avoid strategies leading merely to short term profit. If both individuals take the defection option P, neither will benefit long-term. Our daily behavior follows the former pattern.
- 8.
Many of these dynamics can be verified by simulation. Games are repeated between multiple agents in a simulated society; this approach is known as multi-agent simulation.
References
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Nowak MA (2006) Five rules for the evolution of cooperation. Science 314:1560–1563
Hamilton WD (1963) The evolution of altruistic behavior. Am Nat 97:354–356
Weibull JW (1997) Evolutionary game theory. MIT, Cambridge
Nowak MA (2006) Evolutionary dynamics. Belknap Press of Harvard University Press, Cambridge
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Tanimoto, J. (2014). Dynamics of Non-Linear Systems. In: Mathematical Analysis of Environmental System. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54622-1_4
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DOI: https://doi.org/10.1007/978-4-431-54622-1_4
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