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Dynamics of two-dimensional parabolic discrete map

Xu Qiang Meng Ji-De Bao Bo-Cheng

Dynamics of two-dimensional parabolic discrete map

Xu Qiang, Meng Ji-De, Bao Bo-Cheng
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  • PDF Downloads:  837
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Publishing process
  • Received Date:  06 April 2010
  • Accepted Date:  06 May 2010
  • Published Online:  15 January 2011

Dynamics of two-dimensional parabolic discrete map

  • 1. (1)School of Computer and Information Engineering, Changzhou Institute of Technology, Changzhou 213002, China; (2)School of Electrical and Information Engineering, Jiangsu Teachers University of Technology, Changzhou 213001, China

Abstract: By extending and nonlinearly coupling two one-dimensional parabolic discrete maps, a new two-dimensional parabolic discrete map is achieved. By using stability analysis of fixed points and bifurcation analysis of map, the complex dynamical behavior and attractor evolution of the proposed two-dimensional discrete map are investigated, and its peculiar dynamical characteristics, such as the coexisting bifurcation modes and fast-slow periodic oscillation effects, etc., are illustrated. The research results indicate that two-dimensional parabola discrete map has two control parameters with different functions of adjustable dynamical behaviors and adjustable dynamic amplitudes, and there emerge nonlinear physical phenomena of Hopf bifurcation, bifurcation mode coexisting, locked-frequency and periodic oscillation fast-slow effect. Furthermore, the corresponding theoretical analysis and numerical simulation results are verified based on a digital circuit realized by microcontroller.

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