On the bifurcation of Marotto's map and its application in image encryption

The aim of this paper is to address the codimension-one bifurcation of Marotto's map and its utility in image encryption. First of all, local stability analysis and local bifurcation analysis of fixed points of the considered map are investigated in details. According to the classical bifurcation theory and the center manifold theorem, the map exhibits various bifurcation types such as transcritical, flip and Neimark-Sacker bifurcations. Second of all, the map is proven to be chaotic in the sense of Marotto. Since image encryption based on chaotic maps is very promising for cryptography, Marotto's map, compound chaos, and spatiotemporal chaos are combined to encrypt and decrypt images. Numerical simulations agree with the analytical framework for the complex dynamics of the map. Furthermore, different test images are used to demonstrate the effectiveness of the method implemented for encryption.