New 4D Chaotic System with Infinite Equilibrium and Secure Colour Image Encryption

A new four-dimensional chaotic system is proposed here which has hidden attractors and infinitely many equilibrium points. The nature of the dynamics of the system is studied using bifurcation diagrams, phase portraits and Lyapunov exponent plots. The coexistence of fixed points surrounded by chaotic attractors is realized while fixing the variables and altering the initial values. An amplitude control is investigated for the proposed chaotic system. Concurrently a new algorithm for colour image encryption is developed using the proposed chaotic system. The potential of the algorithm against statistical and differential attacks is confirmed by some fundamental security analysis.