Properties of Some Generalised Logistic Maps with Fractional Exponents

		/vol02/gottlieb/	© Copyright 1995
		Volume 02	Received: Accepted:	---- ----

Properties of Some Generalised Logistic Maps with Fractional Exponents H. P. W. Gottlieb
Abstract
	In contra-distinction to the customary logistic map, for the case of generalised unimodal maps with derivative equal to zero at the origin, the attractor may depend on the initial x value, and the map iterates to zero if this x is too low or too high. Because x = 0 is always a stable fixed point for these maps, bistability is exhibited. The onset of the positive stable fixed point occurs as a positive jump up from zero. After chaos occurs, there is a cut-off value of the control parameter beyond which the attractor is again just zero. A case with near-origin exponent 3/2 is analysed in detail.

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