In order to describe more complex nonlinear dynamic characteristics and obtain chaotic signals that are more suitable for engineering applications

a flux-controlled memristor was used to replace the coupling parameter in the improved four-dimensional Lü chaotic system

and a new five-dimensional memristive hyperchaotic system was proposed. The rich dynamic characteristics of the new system were studied by using conventional nonlinear analysis methods such as phase diagram

bifurcation diagram

and Lyapunov exponential spectrum. On the basis of the new system

by introducing an absolute value function into the system to make it reach a new polarity balance

a new conditionally symmetric memristive hyperchaotic system was constructed. Results show that the new memristive system could exhibit extreme multistability phenomena dependent on the initial states of the memristor

sustained chaotic or hyperchaotic dynamics

and offset-boosting control behaviors. In particular

when changing the system parameters and taking appropriate initial states

a unique coexisting extreme multistability phenomenon was observed. The conditionally symmetric memristive system could generate an infinite number of pairs of coexisting attractors with opposite polarities and similar attractor sizes. The existence and achievability of the new system was verified through circuit simulation using Multisim

so that the hyperchaotic system can be better applied in practical engineering fields such as secure communications.