Design strategies for the creation of aperiodic nonchaotic attractors

TL;DR

This paper presents a method to generate aperiodic, nonchaotic attractors in nonlinear systems through parametric modulation, with experimental validation using electronic circuits, highlighting their fractal geometry and aperiodic dynamics.

Contribution

It introduces a novel procedure for creating aperiodic nonchaotic attractors using random or pseudo-random modulation, supported by experimental implementation.

Findings

Attractors are fractal in geometry.

Dynamics are aperiodic over accessible timescales.

Experimental realization confirms theoretical predictions.

Abstract

Parametric modulation in nonlinear dynamical systems can give rise to attractors on which the dynamics is aperiodic and nonchaotic, namely with largest Lyapunov exponent being nonpositive. We describe a procedure for creating such attractors by using random modulation or pseudo-random binary sequences with arbitrarily long recurrence times. As a consequence the attractors are geometrically fractal and the motion is aperiodic on experimentally accessible timescales. A practical realization of such attractors is demonstrated in an experiment using electronic circuits.