Algebraic approach for the exploration of the onset of chaos in discrete nonlinear dynamical systems

作者：Ragulskis Minvydas^*; Navickas Zenonas; Palivonaite Rita; Landauskas Mantas

来源：Communications in Nonlinear Science & Numerical Simulation, 2012, 17(11): 4304-4315.

DOI：10.1016/j.cnsns.2012.03.017

• Hankel matrix
• Rank of a sequence
• Algebraic decomposition
• Onset of chaos

An algebraic approach based on the rank of a sequence is proposed for the exploration of the onset of chaos in discrete nonlinear dynamical systems. The rank of the partial solution is identified and a special technique based on Hankel matrices is used to decompose the solution into algebraic primitives comprising roots of the modified characteristic equation. The distribution of roots describes the dynamical complexity of a solution and is used to explore properties of the nonlinear system and the onset of chaos.

• 出版日期2012-11