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

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.