Construction of chaotic dynamical system

I. Bula; I. Rumbeniece

doi:10.3846/1392-6292.2010.15.1-8

Construction of chaotic dynamical system

I. Bula^*
, I. Rumbeniece

^*Corresponding author for this work

Department of Mathematics

University of Latvia

Research output: Contribution to journal › Article › peer-review

Abstract

The first-order difference equation x_n+1 = f(x_n), n = 0, 1, where f: R→R, is referred as an one-dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long-term. In this paper we consider family of chaotic mappings in symbol space Σ₂. We use the idea of topological semi-conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic.

Original language	English
Pages (from-to)	1-8
Journal	Mathematical Modelling and Analysis
Volume	15
Issue number	1
DOIs	https://doi.org/10.3846/1392-6292.2010.15.1-8
Publication status	Published - Feb 2010

OECD Field of Science

1.1 Mathematics

Keywords

Binary expansion
Chaotic mapping
Increasing mapping
Infinite symbol space
Topological semi-conjugacy

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10.3846/1392-6292.2010.15.1-8

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AU - Rumbeniece, I.

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AB - The first-order difference equation xn+1 = f(xn), n = 0, 1, where f: R→R, is referred as an one-dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long-term. In this paper we consider family of chaotic mappings in symbol space Σ2. We use the idea of topological semi-conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic.

KW - Binary expansion

KW - Chaotic mapping

KW - Increasing mapping

KW - Infinite symbol space

KW - Topological semi-conjugacy

UR - https://www.tandfonline.com/doi/abs/10.3846/1392-6292.2010.15.1-8

UR - https://www.scopus.com/pages/publications/77951704998

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VL - 15

SP - 1

EP - 8

JO - Mathematical Modelling and Analysis

JF - Mathematical Modelling and Analysis

IS - 1

ER -

Construction of chaotic dynamical system

Abstract

OECD Field of Science

Keywords

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