Linear and rotational fractal design for multiwing hyperchaotic systems with triangle and square shapes

Since the German biochemist Otto Rossler proposed the first hyperchaotic model in the years 1970s and showed to the scientific community how important hyperchaos can be in describing real life phenomena, it has become necessary to develop and propose various techniques capable of generating hyperchaotic attractors with more complex dynamics applicable in both theory and practice. We propose in this paper, an innovative method with analytical and numerical aspects able to generate a class of hyperchaotic attractors with many wings and different shapes. We use a fractal operator to obtain an expression of the modified fractal-fractional Lu system, which is therefore solved numerically. After showing that the initial model is hyperchaotic, we perform some numerical simulations that prove that the hyperchaotic status of the system remain unchanged. The results show that the modified system can generate hyperchaotic attractors of types n-wings, n x m-wings, n x m x pwings and n x m x p x r-wings (m, n, p, r is an element of N), using both linear and rotational variations. It appears that the system is involved in fractal designs comprising a linear or rotational self-duplication process happening in different scales across the system and ending up with the triangular or square shape.(c) 2022 Elsevier Ltd. All rights reserved.