Dynamics of the Zeraoulia-Sprott Map Revisited

where a and b are bifurcation parameters. In the paper “Some Open Problems in Chaos Theory and Dynamics” [4], the following problem was formulated: Find regions in the a–b plane in which the map (1) is bounded and chaotic in the rigorous mathematical definition of chaos and boundedness of attractors. In the present paper, the boundedness of the attractors of the map (1) is studied and the corresponding analytical estimation of absorbing set is obtained, thereby giving an answer to the above problem. Introduce the notation h(yk) = −a 1 + yk , k ∈ N0. (2)