On the Dynamics of a Simple Rational Planar Map

Abstract

The dynamics of the map [Formula: see text] are discussed for various values of its parameters. Despite the simple algebraic structure, this map, recently introduced in the literature, is very rich in nonlinear phenomena. Multiple strange attractors, transitions to chaos via period-doubling bifurcations, quasiperiodicity as well as intermittency, interior crisis, hyperchaos are only a few. In this work, strange attractors, bifurcation diagrams, periodic windows, invariant characteristics are investigated both analytically and numerically.

Hidden attractors in a class of two-dimensional rational memristive maps with no fixed points

“…Meanwhile, rational maps which contain the term of rational fraction have been studied in the literature [38][39][40][41][42][43][44]. In [38], Lu et al investigated the complex dynamics of a class of one-dimensional rational chaotic maps.…”

“…This class of two-dimensional rational maps is called Zeraoulia-Sprott map. Then Somarakis and Baras elaborated the complex dynamics of the Zeraoulia-Sprott map in [42]. In [43], Chen et al analytically gave the boundedness of the attractors and estimated the absorbing set of the Zeraoulia-Sprott map further.…”

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

“…Among different maps, the maps with rational fraction (see e.g., Refs. [34][35][36][37][38][39][40][41]) are complex and it is challenging for investigation. In Ref.…”

“…In Ref. [39], Somarakis and Baras investigated the complex dynamics of the two-dimensional rational map proposed in Ref. [37] analytically and numerically by studying the strange attractors, bifurcation diagrams, periodic windows, and invariant characteristics.…”