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

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.

► The H-rank technique is proposed to decompose the solution into algebraic primitives.
► The distribution of characteristic H-roots describes the dynamical complexity of a partial solution.
► A new algebraic approach is used to explore the onset of chaos in discrete dynamical systems.