The logistic map of matrices

Zenonas Navickas; Rasa Smidtaite; Alfonsas Vainoras; Minvydas Ragulskis

doi:10.3934/dcdsb.2011.16.927

Article Contents

2011, Volume 16, Issue 3: 927-944. Doi: 10.3934/dcdsb.2011.16.927

This issue Previous Article Addendum Next Article Tikhonov's theorem and quasi-steady state

The logistic map of matrices

1.
Department of Applied Mathematics, Kaunas University of Technology, Studentu 50-325, Kaunas LT-51368
2.
Institute of Cardiology, Kaunas University of Medicine, Sukileliu av. 17, LT-50009, Kaunas
3.
Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-222, Kaunas LT-51368

Received: August 31, 2010

Revised: February 28, 2011

Published: September 2011

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Abstract

The standard iterative logistic map is extended by replacing the scalar variable by a square matrix of variables. Dynamical properties of such an iterative map are explored in detail when the order of matrices is 2. It is shown that the evolution of the logistic map depends not only on the control parameter but also on the eigenvalues of the matrix of initial conditions. Several computational examples are used to demonstrate the convergence to periodic attractors and the sensitivity of chaotic processes to initials conditions.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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