By Michael F. Barnsley
ISBN-10: 0120790696
ISBN-13: 9780120790692
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Additional info for Fractals Everywhere, Second Edition
Sample text
6 that the short-term dynamics appears cyclic. 46). We might regard the short-term model as imbedded in the long-term one. 47) xn+l = B(yitb)), where y denotes pollution within a time unit and appropriate functions A, B, and g are to be defined. 47) is independent of n. 8 Salmo n Dynamic s 23 then t - t = 1 - f, - c . 47). Just suppose, for example, that our mischievous polluter achieves his goal by doubling the pollutio n level one tenth of a tim e unit after every reading, lettin g it decay at the natural rat e and then halving it again one tenth of a tim e unit before the next reading.
How good is thi s model ho w realistic are it s assumptions? That’ s an interesting and importan t question, but we’ll put it aside unti l Chapter 4. Meanwhile, if you are unfamilia r wit h diagrams lik e Fig. 3 (or Fig. 5. 5 χ A Secon d Simpl e Ecosyste m Thi s time, let x(t) and y{t) denote th e numbers of thousands (say) of in› dividuals, at tim e t, in populations of tw o species that compete for the same food supply (herbivores for grass, say). 17) still apply, of course, but the model wil l have t o be altered.
The Supplementary Notes sections can be found at the ends of the chapters. 30 Chapte r 1 Growt h and Decay . Dynamica l System * th e greater the number of collisions between respective molecules. I t there› for e seems reasonable t o assume that the rat e at which A and Β are con› verted int o Ρ wil l be proportiona l t o the concentration of each. Let [X] denote the concentration of substance X, in moles per unit volume. Then we have Rate of Increase of Product = Rate of Conversion of Reactant (1-65) k[A)[B) where A: is a constant.
Fractals Everywhere, Second Edition by Michael F. Barnsley
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