Novel memristive hyperchaotic system designs and their engineering applications have received considerable critical attention. In this paper, a novel multistable 5D memristive hyperchaotic system and its application are introduced. The interesting aspect of this chaotic system is that it has different types of coexisting attractors, chaos, hyperchaos, periods, and limit cycles. First, a novel 5D memristive hyperchaotic system is proposed by introducing a flux-controlled memristor with quadratic nonlinearity into an existing 4D four-wing chaotic system as a feedback term. Then, the phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy are used to analyze the basic dynamics of the 5D memristive hyperchaotic system. For a specific set of parameters, we find an unusual metastability, which shows the transition from chaotic to periodic (period-2 and period-3) dynamics. Moreover, its circuit implementation is also proposed. By using the chaoticity of the novel hyperchaotic system, we have developed a random number generator (RNG) for practical image encryption applications. Furthermore, security analyses are carried out with the RNG and image encryption designs.

In this work, a novel 6D four-wing hyperchaotic system with a line equilibrium based on a flux-controlled memristor model is proposed. The novel system is inspired from an existing 5D four-wing hyperchaotic system introduced by Zarei (2015). Fundamental properties of the novel system are discussed, and its complex behaviors are characterized using phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. When a suitable set of parameters are chosen, the system exhibits a rich repertoire of dynamic behaviors including double-period bifurcation of the quasiperiod, a single two-wing, and four-wing chaotic attractors. Further analysis of the novel system shows that the multiple coexisting attractors can be observed with different system parameter values and initial values. Moreover, the feasibility of the proposed mathematical model is also presented by using Multisim simulations based on an electronic analog of the model. Finally, the active control method is used to design the appropriate controller to realize the synchronization between the proposed 6D memristive hyperchaotic system and the 6D hyperchaotic Yang system with different structures. The Routh–Hurwitz criterion is used to prove the rationality of the controller, and the feasibility and effectiveness of the proposed synchronization method are proved by numerical simulations.

At present, design of discrete memristor based chaotic maps starts to attract the attention of the scientists, but it is still in its incipient stage. In this paper, spatiotemporal chaos in the Sine map lattice with discrete memristor coupling is investigated. Firstly, the $3\times m$ higher dimensional chaotic map is proposed, where there are $m$ discrete memristors and $m$ state variable difference items as the inputs of the discrete memristors. Since it is a spatiotemporal chaotic system, thus it can generate massive chaotic sequences according to the system dimension. Secondly, dynamical characteristics of the system is carried out theoretically and numerically. It shows that there are $m$ positive Lyapunov exponents with high complexity. The two examples with one memristor and two memristors are analyzed, and it indicates that the system has rich dynamics including hyperchaos and multistability. Finally, analogue circuit and DSP digital circuit of the two illustrative examples and an Knowm memristor based example are designed to verify the physical realizability of the proposed discrete memristor chaotic maps.

This brief presents the analog circuit of a simplified Tent map and its applications in sensor position optimization. The experimental results of the circuit are consistent with the numerical simulation results. It shows that the system has complex dynamic behaviors. The generated time series from the simplified Tent map is introduced to the PSO (Particle Swarm Optimization) algorithm to enhance its random detection ability. As a result, the modified PSO is employed to the wireless sensor network for sensor position optimization and a more satisfying result is obtained. It indicates that, compared with previous studies about chaotic map, the corresponding analog circuit proposed in this brief is more concise and the chaotic POS algorithm has potential engineering application values.