Dynamics of a New Multistable 4D Hyperchaotic Lorenz System and Its Applications

Using an effective nonlinear feedback controller, a novel 4D hyperchaotic Lorenz system is built. Dynamical analyses show that it has interesting properties. Using some well-known analysis tools like Lyapunov spectrum, bifurcation analysis, chaos diagram, and phase space trajectories, it is found that several bifurcations enable the hyperchaotic dynamics to occur in the introduced model. Also, many windows of heterogeneous multistability are found in the parameter space (i.e. coexistence of a pair of chaotic attractors, coexistence of a periodic and a chaotic attractor). Besides, DSP implementation is successfully used to support the results of the theoretical prediction. Finally, a judicious image encryption algorithm based on the hyperchaotic Lorenz system is proposed with detailed analysis. The effectiveness of the proposed approach is confirmed via several security analyses, which yields a secure image encryption application.