<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a nonsimple structure, supporting an invariant mixing measure. This observation verifies Lasota's conjecture concerning nontrivial ergodic properties of the model.</p></abstract>

We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a nonsimple structure, supporting an invariant mixing measure. This observation verifies Lasota's conjecture concerning nontrivial ergodic properties of the model.

Ergodic theory approach to chaos: Remarks and computational aspects

Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, AGH University of Science and Technology, al. Mickiewicza 30/B-1, 30-059 Cracow, Poland

Department of Automatics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland

International Journal of Applied Mathematics and Computer Science

{"article-title":"Ergodic theory approach to chaos: Remarks and computational aspects"}

We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing...

Ergodic theory approach to chaos: Remarks and computational aspects

Publié en ligne: 28 juin 2012

Pages: 259 - 267

DOI: https://doi.org/10.2478/v10006-012-0019-4

Mots clés
ergodic theory, chaos, invariant measures, attractors, delay differential equations

This content is open access.

Ergodic theory approach to chaos: Remarks and computational aspects

Publié en ligne: 28 juin 2012

Pages: 259 - 267

DOI: https://doi.org/10.2478/v10006-012-0019-4

Mots clésergodic theory, chaos, invariant measures, attractors, delay differential equations

This content is open access.

Mots clés
ergodic theory, chaos, invariant measures, attractors, delay differential equations