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Exploring dynamical systems and chaos using the logistic map model of population change
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10.1119/1.4813114
/content/aapt/journal/ajp/81/10/10.1119/1.4813114
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/10/10.1119/1.4813114

Figures

Image of Fig. 1.
Fig. 1.

(a) Representative trajectories of the logistic equation (2) showing the population as a function of time with (0) = 250,  = 1000, and  = 0.75 (dashed-dotted), 1.75 (dashed), or 2.75 (solid). (b) Representative trajectories of the logistic map (3) showing the population versus generation number with ,  = 1000, and (dashed-dotted), 1.75 (dashed), or 2.75 (solid).

Image of Fig. 2.
Fig. 2.

(a) Representative trajectories of the logistic map (3) showing the population versus generation number with ,  = 1000, and (dashed) or 3.5 (solid). (b)  = 1000, , and (dashed) or (solid).

Image of Fig. 3.
Fig. 3.

(a) Bifurcation diagram for the logistic map (3) with  = 1000. The parameter is the dimensionless population growth factor. (b) Detail for showing the region of parameter space where the logistic map exhibits periodic solutions and deterministic chaos.

Image of Fig. 4.
Fig. 4.

“Cobweb” plots showing (a) a steady-state fixed-point solution, (b) a steady-state period-4 oscillation, and (c) deterministic chaos. Parameters are the same as the solid trajectories in Fig. 1(b) (fixed-point solution), Fig. 2(a) (period-4 oscillations), and Fig. 2(b) (chaos).

Image of Fig. 5.
Fig. 5.

The steady-state dynamics of Eq. (7) are summarized as a function of and . Dots denote stable fixed-point solutions, increasingly dark shades of gray denote periodic solutions of increasing period, white denotes extinction, horizontal lines denotes chaos, and cross-hatching denotes numerical instability yielding solutions that diverge toward infinity or negative infinity.

Tables

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Table I.

Logistic-map-like dynamics of select insect populations with non-overlapping generations determined by Hassell, Lawton, and May by fitting Eq. (13) to field population data sets (Colorado potato beetle and cabbage root fly) or laboratory experiments (Australian sheep blowfly) (Ref. ).

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/content/aapt/journal/ajp/81/10/10.1119/1.4813114
2013-10-01
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Exploring dynamical systems and chaos using the logistic map model of population change
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/10/10.1119/1.4813114
10.1119/1.4813114
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