Analysis of a system of multi-scroll attractors in their mirror & electronic implementation

Abstract

Attractors with multiple wings and many scrolls remain captivating for the number and variety of non-linear bifurcations they display. Then, other features related to these attractors like hyper-chaos, fractal, hidden attractor, strange attractor are also significant. This paper analyzes and implements another important attractors' feature, related to generating their mirror symmetrical projections which also conserve the original properties. The generation of that mirroring process is possible thanks to the perturbation with the duality-symmetrical operator ϵ and the mirror conversion function λ, that have been incorporated into a variable order four dimensional system of chaotic attractors with many scrolls (CAMS). We first solve the model numerically and analyze the committed error then, we study the system's state of disorder, stability and randomness. Numerical simulations are performed and show existence of the model's CAMS in their mirroring structure, where the mirror images share identical properties. Lastly, a programmed circuit implementation is done making used of a digital-to-analog converter (DAC) and a Field Programmable Gate Array (FPGA) board. The obtained digital outputs via the Rigol digital oscilloscope (RDO) correspond to the intended outcomes, those found in the analytical-numerical part of the work.

Keywords

• Multi wing and multi scroll attractor
• Chaos
• Variable order operator
• Mirroring and fractal
• Circuit implementation