The braids: Coexistence of attractors in multi-scroll chaotic system with periodically forced term

This paper proposes a novel three-dimensional chaotic system constructed using only two smooth nonlinear functions: a hyperbolic tangent and a sine functions. Multi-scroll attractors and a single equilibrium point are among the complicated dynamics that the system displays regardless of its simple construction. With a periodically forcing term, the proposed system reveals a new manifestation of megastability, where an infinite countable family of nested braided attractors emerges. These attractors are topologically analyzed using braid theory, linking matrices, and symbolic dynamics, offering insight into their structural complexity. In addition, we investigate the role of fractional-order derivatives in the system, demonstrating how memory effects can qualitatively alter the chaotic behavior. The simplicity and richness of the proposed system make it a valuable model for investigating topological chaos, braid structures, and parameter sensitive dynamics in both integer and fractional order. • A novel multi-scroll chaotic system is constructed using only two hyperbolic-form nonlinear terms. • The system exhibits megastability with coexisting attractors under periodic forcing. • A braiding structure among the attractors is revealed and topologically interpreted. • The influence of fractional-order dynamics behavior is also investigated.