Strongly perturbed bondorbital attractors for generalized systems.

Abstract

This paper analyzes a generalized chaotic system of differential equations characterized by attractors with bondorbital structures. Both classical and fractional-order cases are examined analytically and numerically, with convergence and stability analyses provided. The numerical findings confirm the presence of bondorbital attractors in the classical system. In contrast, bondorbital attractors also emerge in the fractional model employing the Caputo-Fabrizio operator, albeit with significant perturbations for specific fractional orders. To validate these results, an electric circuit implementation of the fractional-order system using an field-programmable gate array board was conducted, yielding consistent outcomes. This study highlights the potential of fractional calculus, particularly the Caputo-Fabrizio operator, in capturing the memory effects and complex dynamics of chaotic systems. The work bridges theoretical modeling and practical hardware applications, offering valuable insights for modeling complex systems.