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.

Multistablity analysis and formation of spiral wave in the fractional-order nonlinear systems is a recent hot topic. In this paper, dynamics, coexisting attractors, complexity, and synchronization of the fractional-order memristor-based hyperchaotic Lü system are investigated numerically by means of bifurcation diagram, Lyapunov exponents (LEs), chaos diagram, and sample entropy (SampEn) algorithm. The results show that the system has rich dynamics and high complexity. Meanwhile, coexisting attractors in the system are observed and hidden dynamics are illustrated by changing the initial conditions. Finally, the network based on the system is built, and the emergence of spiral waves is investigated and chimera states are observed.

Measuring the complexity of time series provides an important indicator for characteristic analysis of nonlinear systems. The permutation entropy (PE) is widely used, but it still needs to be modified. In this paper, the PE algorithm is improved by introducing the concept of the network, and the network PE (NPE) is proposed. The connections are established based on both the patterns and weights of the reconstructed vectors. The complexity of different chaotic systems is analyzed. As with the PE algorithm, the NPE algorithm-based analysis results are also reliable for chaotic systems. Finally, the NPE is applied to estimate the complexity of EEG signals of normal healthy persons and epileptic patients. It is shown that the normal healthy persons have the largest NPE values, while the EEG signals of epileptic patients are lower during both seizure-free intervals and seizure activity. Hence, NPE could be used as an alternative to PE for the nonlinear characteristics of chaotic systems and EEG signal-based physiological and biomedical analysis.

In this paper, dynamics and complexity of the integer-order and fractional-order centrifugal flywheel governor systems are investigated numerically by the bifurcation diagram, Lyapunov exponents (LCEs), chaos diagram and spectral entropy (SE) algorithm separately. Moreover, the effect of periodic force and stochastic noise on the dynamics and complexity of the integer-order and fractional-order systems also are analyzed. Finally, the multistability of the system is discussed by coexisting attractors and the basins of attraction. The results show that the fractional-order system has rich dynamical behaviours. Stochastic noise has a great effect on dynamics and complexity of the integer-order and fractional-order systems. The high complexity region is determined and SE complexity can indicate different state of the system effectively. And the integer-order and fractional-order systems show multistability with the variation of initial conditions.

Multistability in a Fractional-Order Centrifugal Flywheel Governor System and Its Adaptive Control: In this paper, a 4D fractional-order centrifugal flywheel governor system is proposed. Dynamics including the multistability of the system with the variation of system parameters and the derivative order are investigated by Lyapunov exponents (LEs), bifurcation diagram, phase portrait, entropy measure, and basins of attraction, numerically. It shows that the minimum order for chaos of the fractional-order centrifugal flywheel governor system is q=0.97, and the system has rich dynamics and produces multiple coexisting attractors. Moreover, the system is controlled by introducing the adaptive controller which is proved by the Lyapunov stability theory. Numerical analysis results verify the effectiveness of the proposed method.