Abstract
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.
Highlights
Chaotic oscillators have been a hot topic for research during the last years due to its usefulness in the development of chaotic secure communication systems and other applications that have been implemented using either analog or digital electronics, as already shown in [1]
A 3-D CHAOTIC SYSTEM WITH PEANUT-SHAPED SYMMETRIC EQUILIBRIUM CURVE In this work, we describe a new 3-D system with peanutshaped symmetric equilibrium curve, which is given by the following dynamics:
We analyzed the dynamical properties of the new chaotic system using bifurcation analysis of the system parameters and an entropy analysis of the system
Summary
Chaotic oscillators have been a hot topic for research during the last years due to its usefulness in the development of chaotic secure communication systems and other applications that have been implemented using either analog or digital electronics, as already shown in [1]. MULTISTABILITY AND COEXISTING ATTRACTORS Figure 6 shows the phase diagram of the new chaotic system (1) for different values of parameters a and b.
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