A new multistable jerk system with Hopf bifurcations, its electronic circuit simulation and an application to image encryption

Abstract

In this work, we announce a new 3-D jerk system and show that it is chaotic and dissipative with the calculation of the Lyapunov exponents of the system. By performing a detailed bifurcation analysis, we observe that the new jerk system exhibits Hopf bifurcations. It is also shown that the new jerk system exhibits multistability behaviour with two coexisting chaotic attractors. An electronic circuit simulation of the jerk system is built using Multisim. Finally, we design a new approach to image encryption as a cryptographic application of our chaotic jerk system. The simulation outcomes prove the efficiency of the proposed encryption scheme with high security.