A new auto-replication in systems of attractors with two and three merged basins of attraction via control

Largely recognized as leading concepts in network traffic prediction, machining or image processing, the processes of auto-duplication, self-organization and auto-replication are highly useful and fascinating for chaos and fractal theorists. Those processes appear naturally around us as observed on trees, river deltas, lightning, growth spirals, flowers, romanesco broccoli, frost, etc. Using mathematical notions, concepts and processes to reproduce and control auto-duplication and auto-replication dynamics have attracted the attention of scientists and engineers given their wide range of applications. We use the control technique combined to two different concepts, Julia's process and fractal-fractional operator, to generate auto-replication in systems of chaotic attractors with two and three merged basins of attraction. The systems used here comprise a controller part, namely the switching-manifold control. Both systems are solved numerically using Julia's scheme and Legendre wavelets methods. Numerical simulations reveal a fascinating capability for the systems to auto-replicate while conserving the initial properties of the systems, such as symmetry and number of basins of attraction. The merged basins of attraction are shown to be moving away as the result of the fractional dynamics' impact. Great results that may interest scientists and engineers dealing with fractals and chaos. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

The processes of auto-duplication and auto-replication play a significant role in chaos and fractal theories, allowing for the reproduction of systems while conserving their initial properties. Researchers utilize concepts like Julia's process and fractal-fractional operator to create self-replicating systems, holding potential interest for scientists and engineers.