Initial-condition effects on ReLU-type hyper-jerk system and its application in image encryption

Abstract

Abstract：The memristive hyper-jerk system described in this study has a non-smooth Rectified Linear Unit (ReLU) memductance function. A non-smooth memductance function of this kind might cause the system to have three line equilibria within it, bring about the arrival of extreme multistability with infinitely many coexisting attractors. Analyzing the three line equilibria’s stabilities and researching the intricate dynamical effects triggered by memristor and non-memristor initial conditions are related topic. Phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and the basins of attraction all show the dynamical tendencies. According to the results, the novel system’s dynamical behaviors depend on both the memristor initial condition and the non-memristor initial conditions. Moreover, PSIM circuit simulations and MCU-based hardware measurements are run to confirm the coexisting infinitely many attractors. The ReLU-type hyper-jerk system is then utilized to encrypt images. Experimental findings support its exceptional robustness against a range of potential attacks. 

A memristive system: dynamics, synchronization, parameter modulation and demodulation

“…Since the memristor was found, it has been applied in various fields, such as in communication system [1], image processing [2,3], integrated circuit [4] and neural networks and et al [5]. what's more, a lot of memristor-based systems have been proposed [6].…”