A controllable 3D hyperchaotic map with infinite coexisting attractors and its application to image encryption

By introducing sinusoidal function feedback on nonlinear system, a controllable 3D hyperchaotic map with rich dynamics is proposed. Amplitude control and offset boosting is used to control the output of the system. Moreover, the homogenous multistability of the proposed 3D model is studied, in which the initial data determines the position of the “scarve” attractor. In view of the rich dynamic characteristics of the model and the randomness of the output sequence, an image encryption scheme is proposed as an application based on chaos. The security of image encryption scheme is simulated numerically, and the results show that the proposed model can be effectively applied to information security.