Design and circuit implementations of multimemristive hyperchaotic system

To enhance the order and Kolmogorov entropy of the memristive hyperchaotic system and improve the realizability of the circuit, a sixth-order memristive hyperchaotic system that consists of two flux-controlled memristors and one charge-controlled memristor is designed. Combined with Lyapunov exponential spectrum, phase trajectory diagram and bifurcation diagram, dynamic characteristics of the system are analyzed, and the effects of system control parameters and initial state on the system dynamic behavior are explored. Equivalent circuit models of flux-controlled and charge-controlled memristors with cubic nonlinear characteristics are constructed by the basic operation modules, and the hardware simulation design of the memristive hyperchaotic system is completed. The experimental results show that the proposed system can exhibit kinds of attractors, such as periodic-loop, single-scroll, double-scroll and superposition by adjusting system control parameters. and the system can show the behavior of period doubling bifurcation entering chaos and anti-period doubling exiting chaos under the different system initial states, which corresponds to the multistable coexistence phenomena of the system, such as quasi-period and hyperchaos. Meanwhile, the sixth-order hyperchaotic system is implemented by hardware circuit simulation. The phase diagrams of the circuit simulation are consistent with that of the numerical simulation, which verifies the physical realizability of the hyperchaotic system. Based on the strong initial value sensitivity and large K entropy, the memristive hyperchaotic system can be applied to the image encryption, and the confidentiality and security of images can be effectively enhanced. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a sixth-order memristive hyperchaotic system is designed to enhance the order and Kolmogorov entropy, and improve the realizability of the circuit. The dynamic characteristics of the system are analyzed through Lyapunov exponential spectrum, phase trajectory diagram, and bifurcation diagram, and the effects of system control parameters and initial state on the system dynamic behavior are explored. Equivalent circuit models of flux-controlled and charge-controlled memristors are constructed, and the hardware simulation design is completed. The experimental results demonstrate that the proposed system can exhibit various attractors and show the behavior of period doubling bifurcation entering chaos and anti-period doubling exiting chaos. The physical realizability of the hyperchaotic system is verified through hardware circuit simulation. The memristive hyperchaotic system can be applied to image encryption to enhance the confidentiality and security of images based on its strong initial value sensitivity and large K entropy.