Chaos On A Simple Rational Planar Map

The dynamics of a 2-D rational map are studied for various values of it’s control parameters. Despite it’s simple structure this model is very rich in non-linear phenomena such as, multi-scroll strange attractors, transitions to chaos via period doubling bifurcations, quasi-periodicity as well as intermittency, interior crisis, hyper-chaos etc. In this work, strange attractors, bifurcation diagrams, periodic indows, invariant characteristics are investigated both analytically and numerically.