A novel multi-stable sinusoidal chaotic map with spectacular behaviors

Abstract

Chaotic behavior can be observed in continuous and discrete-time systems. This behavior can appear in one-dimensional nonlinear maps; however, having at least three state variables in flows is necessary. Due to the lower mathematical complexity and computational cost of maps, lots of research has been conducted based on them. This paper aims to present a novel one-dimensional trigonometric chaotic map that is multi-stable and can act attractively. The proposed chaotic map is first analyzed using a single sinusoidal function; then, its abilities are expanded to a map with a combination of two sinusoidal functions. The stability conditions of both maps are investigated, and their different behaviors are validated through time series, state space, and cobweb diagrams. Eventually, the influence of parameter variations on the maps’ outputs is examined by one-dimensional and two-dimensional bifurcation diagrams and Lyapunov exponent spectra. Besides, the diversity of outputs with varying initial conditions reveals this map’s multi-stability. The newly designed chaotic map can be employed in encryption applications.