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Based on a 5D two-wing hyperchaotic system with dual memristors, a new unified 5D four-wing hyperchaotic system based on dual memristors is proposed, which has four cases and can exhibit three different structures of four-wing attractors. This paper studies the dynamic behaviors of one of these cases by the phase diagrams, bifurcation diagrams, Lyapunov exponents, etc. Of particular surprise, this system has a space equilibrium and can exhibit the two groups of extreme multistability phenomenon of symmetric distribution about the origin. In addition, the striking and complex memristor initial boosting behaviors are investigated in this paper, which shows that the interesting phenomenon is nonlinear and different attractor structures with four-wing and two-wing. When a single parameter is changed, the initial boosting behavior has obvious changes, indicating the memristive initial conditions and parameters have an important influence on the position shift of the attractors. Finally, the new four-wing system is realized by Multisim circuit simulation, which verifies the feasibility of the new system.

An exhaustive analysis of a four-wing chaotic system is presented in this paper. It is proved that the evolution range of some variables can be modulated easily by one coefficient of a cross product term. An amplitude-adjustable chaotic circuit is designed, which shows a good agreement with the theoretical analysis. Also, in this paper a microcontroller-based random number generator (RNG) was designed with a nonlinear four-wing chaotic system. RNG studies of the current time have been usually carried out with complicated structures that are costly and difficult to use in real time implementations and that require so much energy consumption. On the other hand, in this paper, as opposed to the disadvantages mentioned here, a microcontroller-based RNG was designed with a four-wing chaotic system (also discussed in the paper) and this was introduced to literature. Microcontroller-based random numbers that passed randomness tests will be available for use in many fields in real life, particularly in encryption.

Some basic dynamical behaviors and the compound structure of a new four-dimensional autonomous chaotic system with cubic nonlinearities are investigated. A four-wing chaotic attractor is observed numerically. This attractor, however, is shown to be an numerical artifact by further theoretical analysis and analog circuit experiment. The observed four-wing attractor actually has two coexisting (upper and lower) attractors, which appear simultaneously and are located arbitrarily closely in the phase space. By introducing a simple linear state-feedback control term, some symmetries of the system and similarities of the linearized characteristics can be destroyed, thereby leading to the appearance of some diagonal and anti-diagonal periodic orbits, through which the upper and lower attractors can indeed be merged together to form a truly single four-wing chaotic attractor. This four-wing attractor is real; it is further confirmed analytically, numerically, as well as electronically in the paper. Moreover, by introducing a sign-switching control function, the system orbit can be manipulated so as to switch between two equilibria or among four equilibria, generating two one-side double-wing attractors, which can also be merged to yield a real four-wing attractor.

Although multiwing hidden attractor chaotic systems have attracted a lot of interest, the currently reported multiwing hidden attractor chaotic systems are either with no equilibrium point or with an infinite number of equilibrium points. The multiwing hidden attractor chaotic systems with stable equilibrium points have not been reported. This paper reports a four-wing hidden attractor chaotic system, which has only one stable node-focus equilibrium point. The novel system can also generate a hidden attractor with one-wing and hidden attractors with quasi-periodic and periodic coexistence. In addition, a self-excited attractor with one-wing can be generated by adjusting the parameters of the novel system. The hidden attractors of the novel system are verified by the cross-section of attraction basins. And the hidden behavior is investigated by choosing different initial states. Moreover, the coexisting transient four-wing phenomenon of the self-excited one-wing attractor system is studied by the time domain waveforms and attraction basin. The dynamical characteristics of the novel system are studied by Lyapunov exponents spectrum, bifurcation diagram and Poincaré map. Furthermore, the novel hidden attractor system with four-wing and one-wing are implemented by electronic circuits. The hardware experiment results are consistent with the numerical simulations.

In this paper, based on the Central Manifold Theorem and Hopf Theorem, the Hopf bifurcation characteristics of a novel 3D-chaotic system with a four-wing attractor are studied. The stability of the equilibria of the system is examined. Additionally, the dynamics near the equilibria at infinity are explored using Poincaré compactification on polynomial vector fields in ${ℝ}^3$. These findings contribute to a deeper understanding of the system’s dynamics and provide insights into the behavior of its solutions.