A new four-valued memristive hyperchaotic system with hidden attractors and multistability

Abstract A four-valued memristor is designed based on the memristor model and introduced into a three-dimensional chaotic system to construct a four-dimensional four-valued memristive chaotic system, and its dynamics are investigated and discussed. The properties of the system such as phase diagrams, Poincaré map, dissipation, equilibrium points stability, Lyapunov exponents, Lyapunov dimensions, dynamical complexity, offset boosting, inversion properties, and attractor coexistence are investigated. The system is found to have infinitely many equilibrium points with hidden attractors, and has higher dimensionality, and complexity than the original system. As the parameters change, the new system transitions from a quasi-periodic state to a chaotic state to a hyperchaotic state and finally back to a quasi-periodic state through a reverse period-doubling bifurcation. The complexity of the system is verified using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> algorithm and the spectral entropy algorithm. The offset boosting control of the system can be realized by adding parameters to the system. The system also has phase reversal characteristics of a single parameter control system attractor, and there are multiple types of attractors coexisting with changes in the system parameters at different initial values. In addition, when the parameters of the system are fixed, the existence of exterme multistability based on the initial value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>w</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> the memristor is found. Finally, the feasibility of the design and the correctness of the analysis are verified by simulated circuits. Therefore, the system is highly complex and can be applied in the fields of image encryption and confidential communication.