A Novel 3-D Jerk System, Its Bifurcation Analysis, Electronic Circuit Design and a Cryptographic Application

Abstract

This paper introduces a new chaotic jerk system with three cubic nonlinear terms. The stability properties of the three equilibrium points of the proposed jerk system are analyzed in detail. We show that the three equilibrium points of the new chaotic jerk system are unstable and deduce that the jerk system exhibits self-excited chaotic attractors. The bifurcation structures of the proposed jerk system are investigated numerically, showing period-doubling, periodic windows and coexisting bifurcations. An electronic circuit design of the proposed jerk system is designed using PSPICE. As an engineering application, a new image-encryption approach based on the new chaotic jerk system is presented in this research work. Experimental results demonstrate that the suggested encryption mechanism is effective with high plain-image sensitivity and the reliability of the proposed chaotic jerk system for various cryptographic purposes.

On Hopf and Fold Bifurcations of Jerk Systems

“…An equilibrium point of system (14) has the form E(x 0 , 0, 0), where x 0 is a solution of the equation βX + sX 2 + O(X 3 ) = 0. A solution is x 1 = 0, and the others satisfy F(β, X) = 0 near (0, 0), where F(β, X) = β + sX + X 2 ϕ(X, β).…”

“…Bifurcations of particular jerk systems were analyzed (see, e.g., [7][8][9][10][11]). Moreover, new chaotic jerk systems were recently reported (see, e.g., [12][13][14]).…”

Enhanced Color Image Encryption Utilizing a Novel Vigenere Method with Pseudorandom Affine Functions

“…Hence, the key must satisfy various criteria, encompassing considerations such as length, space, and complexity [10,11]. This implies that the user-inputted key for image encryption needs preprocessing to generate a more intricate form, such as a pseudorandom sequence [12]. However, these keys can also be changed by simply performing standard operations, such as rearranging the image stream [13].…”

On a Family of Hamilton–Poisson Jerk Systems

“…can model processes characterized by changes in acceleration. Despite their simple form, jerk systems provide examples of chaotic behavior (see, e.g., [2][3][4]). Bifurcations in the dynamics of jerk systems are also analyzed (see, e.g., [5][6][7][8]).…”