A locally active discrete memristor model and its application in a hyperchaotic map

© 2022 Springer Nature Switzerland AG. Part of Springer Nature. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s11071-021-07132-5The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi-periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.Peer reviewedFinal Accepted Versio

Research on Information Identification of Chaotic Map with Multi-Stability

Influenced by the rapid development of artificial intelligence, the identification of chaotic systems with intelligent optimization algorithms has received widespread attention in recent years. This paper focuses on the intelligent information identification of chaotic maps with multi-stability properties, and an improved sparrow search algorithm is proposed as the identification algorithm. Numerical simulations show that different initial values can lead to the same dynamic behavior, making it impossible to stably and accurately identify the initial values of multi-stability chaotic maps. An identification scheme without considering the initial values is proposed for solving this problem, and simulations demonstrate that the proposed method has the highest identification precision among seven existing intelligent algorithms and a certain degree of noise resistance. In addition, the above research reveals that chaotic systems with multi-stability may have more potential applications in fields such as secure communication

Improved Chaotic Quantum-Behaved Particle Swarm Optimization Algorithm for Fuzzy Neural Network and Its Application

Traditional fuzzy neural network has certain drawbacks such as long computation time, slow convergence rate, and premature convergence. To overcome these disadvantages, an improved quantum-behaved particle swarm optimization algorithm is proposed as the learning algorithm. In this algorithm, a new chaotic search is introduced, and benchmark function experiments prove it outperforms the other five existing algorithms. Finally, the proposed algorithm is presented as the learning algorithm for Takagi–Sugeno fuzzy neural network to form a new neural network, and it is utilized in the water quality evaluation of Dongjiang Lake of Hunan province. Simulation results demonstrated the effectiveness of the new neural network

Parameter Identification of Fractional-Order Discrete Chaotic Systems

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Chaotic attractor with varied parameters

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Hidden dynamics, synchronization, and circuit implementation of a fractional-order memristor-based chaotic system

Fractional calculus has always been regarded as an ideal mathematical tool to describe the memory of complex systems and special materials. A fractional-order memristor-based chaotic system with hidden dynamics is studied in this paper. The system can exhibit excellent dynamic behavior by introducing a quadratic nonlinear memristor. Asymmetric coexistence occurs when both the order and parameter change. Considering the practical application of fractional-order system, the spectral entropy (SE) algorithm is used to investigate the complexity of the system. Besides, synchronous experiment between two fractional-order system is carried out and the synchronization circuit is also designed. To verify the numerical simulation results, the hardware circuit is constructed, and the hidden attractors are successfully captured on the oscilloscope by hardware electronic circuit

Discrete Memristor and Discrete Memristive Systems

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Gene expression network reconstruction using microarray data is widely studied aiming to investigate the behavior of a gene cluster simultaneously. Under the Gaussian assumption, the conditional dependence between genes in the network is fully described by the partial correlation coefficient matrix. Due to the high dimensionality and sparsity, we utilize the LEP method to estimate it in this paper. Compared to the existing methods, the LEP reaches the highest PPV with the sensitivity controlled at the satisfactory level. A set of gene expression data from the HapMap project is analyzed for illustration