A new 3-D chaotic dynamical system with a peanut-shaped closed curve of equilibrium points is introduced in this work. Since the new chaotic system has infinite number of rest points, the new chaotic model exhibits hidden attractors. A detailed dynamic analysis of the new chaotic model using bifurcation diagrams and entropy analysis is described. The new nonlinear plant shows multi-stability and coexisting convergent attractors. A circuit model using MultiSim of the new 3-D chaotic model is designed for engineering applications. The new multi-stable chaotic system is simulated on a field-programmable gate array (FPGA) by applying two numerical methods, showing results in good agreement with numerical simulations. Consequently, we utilize the properties of our chaotic system in designing a new cipher colour image mechanism. Experimental results demonstrate the efficiency of the presented encryption mechanism, whose outcomes suggest promising applications for our chaotic system in various cryptographic applications.

First, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L₁= 0.0395,L₂= 0 and L₃= −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is D_KY=3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.