Abstract
Consider two populations, x and y, that are interacting either by competition, or as predator and prey. They may end up near a stable steady state, or possibly in seasonally oscillating states; this could depend on their proliferation rates, death rates, available resources, climate change, etc. In this chapter we wish to explore these varied possibilities using mathematics. To do that we begin by a short introduction to the theory of bifurcations. Bifurcation theory is concerned with the question of how the behavior of a system which depends on a parameter p changes with the parameter. It focuses on any critical value, p = p cr , where the behavior of the system undergoes radical change; such values are called bifurcation points.
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Chou, CS., Friedman, A. (2016). Bifurcation Theory. In: Introduction to Mathematical Biology. Springer Undergraduate Texts in Mathematics and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-29638-8_11
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DOI: https://doi.org/10.1007/978-3-319-29638-8_11
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