Robustification of Chaos in 2D Maps

Robust chaos is defined as the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space since the existence of such windows in the chaotic region implies fragility of the chaos. In this paper, we introduce a new terminology called robustification of chaos, which means creating robust chaos (in the sense of the above definition) in a dynamical system. As a first step, a new chaotification (robustification) method to generate robust chaos in planar maps is presented using simple piecewise smooth feedback to create a border collision bifurcation in the resulting system under some realizable conditions. The results are applied to an elementary example to illustrate the validity of the proposed method.