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Paper details
Number 2 - June 2012
Volume 22 - 2012
Ergodic theory approach to chaos: Remarks and computational aspects
Paweł J. Mitkowski, Wojciech Mitkowski
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.
Keywords
ergodic theory, chaos, invariant measures, attractors, delay differential equations