Populations of Attracting-Cycle Oscillators

Abstract

Chapter 4 provides a preliminary look at the phenomena to which we now turn: the phenomena typical of aggregates of oscillators. Just as the oscillator populations of physics comprise a very special case with very special properties (associated with linearity, energy conservation, etc.), so did the simple clocks of Chapter 4 comprise another very special case with very special properties (associated with the one-dimensionality of their state space). My objective in this chapter is to organize under the same four headings as in Chapter 4 some discussions and examples of what I take to be the characteristic behavior of attracting-cycle oscillators in populations and communities. Such oscillators can have any number (≥2) of variables mutually determining their rates of change in nonlinear ways. Linear oscillators, conservative oscillators, and simple clocks are special limiting cases of the attracting-cycle oscillators considered in this chapter.

There was a door to which I found no key.

There was a veil past which I could not see

The Rubiyat of Omar Khayyam