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Chapter 2 Deterministic chaos

DOI: 10.1016/s0167-4137(01)80004-4
  • Ecology
  • Mathematics


Publisher Summary Chaos is usually defined as a random looking motion generated by a simple deterministic process. This chapter discusses the basic concepts and vocabulary regarding chaos. It selects the logistic difference equation as a sample model to explain chaos. This is an orthodox method originally described by May, who initiated the growing interest in chaos. The simplest dynamic model that exhibits chaotic motion is the logistic difference equation. The logistic difference equation is familiar as a population growth model, with numerous ecological applications. In this chapter, however, it is necessary to understand this equation simply as a way of describing a rule governing changes of value Xn in a sequence. The logistic difference equation, which is a one-dimensional discrete dynamical system, produces chaos. Many other models of discrete dynamical systems have been proposed. For example, the models of Ricker and Hassell, are also well-known population growth models. Several examples of difference and differential equations generating chaos are described in this chapter.

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