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Chaos in some planar nonautonomous polynomial differential equation

100%

Wójcik K.

Annales Polonici Mathematici

2000

tom 73

nr 2

159-168

We show that under some assumptions on the function f the system $ż = z̅(f(z) e^{iϕt} + e^{i2ϕt})$ generates chaotic dynamics for sufficiently small parameter ϕ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.

Ergodic theory approach to chaos: Remarks and computational aspects

88%

Mitkowski P., Mitkowski W.

International Journal of Applied Mathematics and Computer Science

2012

tom 22

nr 2

259-267

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 International Journal of Applied Mathematics and Computer Science

1 Mitkowski P.

1 Mitkowski W.

1 Wójcik K.

1 2012

1 2000

Wyniki wyszukiwania

Chaos in some planar nonautonomous polynomial differential equation

Ergodic theory approach to chaos: Remarks and computational aspects