On Fractal Patterns for Multi-Winghyperchaotic Attractors With a Mirrorsymmetrical Structure

Hyperchaos remains one of the most complex behaviors in the bifurcation mechanisms and so far, only few hyperchaotic dynamics have been identified experimentally. The construction and design of complex models able to generate hyperchaotic attractors with wings on many rows and columns have become a source of interest for many fractal & chaos theorists, applied physicists and engineers. In this paper, we make use of a simple method, that consists on combining the fractal and fractional operator with L system, in order to generate second class hyperchaotic attractors with wings on many rows and columns. Such a combination yields a modified initial value problem, that is solved both analytically and numerically. We then implement the proposed scheme to perform some graphical representations showing the second class types of attractors in the form n m-wings, (n, m N), which appear to be hyperchaotic and exhibit a mirror symmetrical structure. The graphical simulations also depict a process where the lower and upper parts of the second class hyperchaotic attractors are seen to be moving away from the mirror symmetrical junction due to the parameter's impact of the fractal-fractional operator.