# 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.

## Key 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.