Multistability and Bifurcation Analysis of a Novel 3D Jerk System: Electronic Circuit Design, FPGA Implementation, and Image Cryptography Scheme

In this paper, we propose a novel 3-D jerk system with three quadratic nonlinear terms and demonstrate the dynamical properties of the proposed jerk system in terms of phase portraits, bifurcation diagrams, Lyapunov exponents, multistability and coexisting attractors. For practical implementations, we apply Multisim version 14.0 to design an electronic model of the proposed 3-D jerk system. To demonstrate the feasibility of the proposed chaotic jerk system, we implement the system using a field-programmable gate array (FPGA), which shows high throughput and low power consumption. Furthermore, a new image encryption scheme based on the proposed jerk system is developed, which involves permutation and diffusion operations. Experimental results and security analysis show the effectiveness of our proposed algorithm in terms of high security and excellent encryption performance.