A simple method to enlarge a basin of attraction using a memristive function

TL;DR

This paper introduces a novel method that employs a memristive function within discrete dynamical systems to enlarge basins of attraction, thereby stabilizing chaotic attractors more effectively without explicit parameter control.

Contribution

The study proposes a new approach using memristors and sigmoid functions to enlarge attraction basins in chaotic systems, demonstrated with the Hénon map.

Findings

Enhanced attractor stability confirmed through simulations

Method enlarges basins of attraction without explicit parameter tuning

Applicable to chaotic systems like the Hénon map

Abstract

This study presents an innovative approach to chaotic attractor stabilization introducing a memristor in discrete dynamical systems. Using the H\'enon map as a test case, we replace a system parameter with a memristive function governed by a sigmoid activation function. The method relies on leveraging attractors with larger basins of attraction to attract the orbits and guide them towards the desired chaotic attractor. The effectiveness of the method is confirmed through numerical simulations, showing substantial enhancement in attractor stability without requiring explicit parameter control.