An Initial-Controlled Double-Scroll Hyperchaotic Map

Abstract Initial condition-dominated offset boosting provides a special channel to arrange coexisting orbits. Due to the nonlinearity and inherent periodicity, sinusoidal function is often introduced into a dynamical system for multistability design. In this paper, an initial-controlled double-scroll hyperchaotic map is constructed based on two sine functions. Four patterns of the double-scroll hyperchaotic orbits are found as 0-degree, 90-degree, 45-degree and 135-degree. Consequently, different modes for attractor growing are demonstrated. Finally, hardware experiments based on STM32 are carried out to verify the theoretical analysis and numerical simulation.