A class of two-dimensional rational maps with self-excited and hidden attractors

This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model these is firstly formulated by introducing term. analysis existence stability the fixed points in suggests that there are four types points, i.e., no point, one single two line points. To investigate complex dynamics with different numerical tools, such as time histories, phase portraits, basins attraction, Lyapunov exponent spectrum, (Kaplan–Yorke) dimension bifurcation diagrams, employed. Our extensive simulations identify both attractors, which were rarely reported literature. Therefore, multi-stability maps, especially one, further explored present work.