Strange Attractors: Creating Patterns in Chaos

Sprott, J. C.; Abraham, Ralph

doi:10.1119/1.17885

Cited by 48 publications

(40 citation statements)

References 13 publications

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“…or quasiperiodicity (for D KY 2) and noninteger values corresponding to strange (fractal) attractors [11,12]. From this information as well as calculations of the eigenvalues of the coexisting equilibrium, state-space plots, and Poincaré sections, the attractor type has been identified and catalogued in Table I.…”

Section: Routes To Chaosmentioning

confidence: 99%

A simple spatiotemporal chaotic Lotka–Volterra model

Sprott

Wildenberg

Azizi

2005

Chaos, Solitons & Fractals

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Section: Routes To Chaosmentioning

confidence: 99%

A simple spatiotemporal chaotic Lotka–Volterra model

Sprott

Wildenberg

Azizi

2005

Chaos, Solitons & Fractals

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“…Many different types of fractals were found: fractals generated through Iterated Function Systems [3], L-systems [25], strange attractors [31], complex fractals [3], etc.…”

Section: Introductionmentioning

confidence: 99%

Biomorphs via modified iterations

Gdawiec¹,

Kotarski²,

Lisowska³

2016

J. Nonlinear Sci. Appl.

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The aim of this paper is to present some modifications of the biomorphs generation algorithm introduced by Pickover in 1986. A biomorph stands for biological morphologies. It is obtained by a modified Julia set generation algorithm. The biomorph algorithm can be used in the creation of diverse and complicated forms resembling invertebrate organisms. In this paper the modifications of the biomorph algorithm in two directions are proposed. The first one uses different types of iterations (Picard, Mann, Ishikawa). The second one uses a sequence of parameters instead of one fixed parameter used in the original biomorph algorithm. Biomorphs generated by the modified algorithm are essentially different in comparison to those obtained by the standard biomorph algorithm, i.e., the algorithm with Picard iteration and one fixed constant.

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“…On the other hand, dynamics of discrete-time maps, such as the Logistic map and the Hénon map, have been studied extensively in different disciplines fueled by their broad applications in economics, biology, and engineering (see [25][26][27][28] for examples). However, there are very few results on hidden attractors in discrete-time maps.…”

Section: Introductionmentioning

confidence: 99%