15 research outputs found

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

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    © 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

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    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

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    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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    Research on fractional-order discrete chaotic systems has grown in recent years, and chaos synchronization of such systems is a new topic. To address the deficiencies of the extant chaos synchronization methods for fractional-order discrete chaotic systems, we proposed an improved particle swarm optimization algorithm for the parameter identification. Numerical simulations are carried out for the Hénon map, the Cat map, and their fractional-order form, as well as the fractional-order standard iterated map with hidden attractors. The problem of choosing the most appropriate sample size is discussed, and the parameter identification with noise interference is also considered. The experimental results demonstrate that the proposed algorithm has the best performance among the six existing algorithms and that it is effective even with random noise interference. In addition, using two samples offers the most efficient performance for the fractional-order discrete chaotic system, while the integer-order discrete chaotic system only needs one sample

    Chaotic attractor with varied parameters

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    Based on the parameter estimation technologies of the chaotic systems, and the chaotic systems which produce chaotic attractors while their parmeters are varied, a new model of the chaotic attractors is proposed. The parameters of the proposed model are varied as same as the state variables of the traditional chaotic attractors. The variation ranges and values of the varied parameters are designed to produce the required chaotic attractors. As the parameter variation of the chaotic systems affects the chaotic attractors, it also affects the Lyaponov exponents and the complexity of the chaotic systems. It affects the construction methods of the chaotic attractor by affecting the point equilibria of the attractor. The results of the numerical simulation show that the variation process of the parameters can positively affect the sensitivity of the system to its initial conditions, which increase the values of the largest Lyapunov exponent. It also stabilizes the complexity level throughout the range of the varied parameters

    Modeling different discrete memristive sine maps and its parameter identification

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    Compared with the continuous chaotic system designed by analog circuit, chaotic maps realized by the digital circuit has the characteristics of simple logic and easy implementation, so it has attracted more attention in engineering applications. How to construct the chaotic map with simple structure and strong complexity behaviors has always been a research hotspot. Recently, the concept of discrete memristor receives growing discussion. Existing studies have found that introducing it into classical chaotic map can enhance its chaotic characteristics. In this paper, three discrete memristor mathematical models are summarized. These models are introduced into the classical sine map, and three new two-dimensional discrete memristive sine maps are constructed. Dynamic analysis demonstrate the effect of the discrete memristor in improving the chaos characteristics. The proposed new systems not only expand the scope of chaos, but also greatly improve the Lyapunov exponent value, and appear hyperchaotic behavior and coexisting attractors. Through the parameter identification technology, the proposed discrete memristive chaotic maps are compared with several existing chaotic maps. The identification simulations show that the proposed chaotic maps have lower identification rate, so their security is higher

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

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    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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    In this paper, we investigate the mathematical models of discrete memristors based on Caputo fractional difference and G–L fractional difference. Specifically, the integer-order discrete memristor is a special model of those two cases. The “∞”-type hysteresis loop curves are observed when input is the bipolar periodic signal. Meanwhile, numerical analysis results show that the area of hysteresis decreases with the increase of frequency of input signal and the decrease of derivative order. Moreover, the memory effect, characteristics and physical realization of the discrete memristors are discussed, and a discrete memristor with short memory effects is designed. Furthermore, discrete memristive systems are designed by introducing the fractional-order discrete memristor and integer-order discrete memristor to the Sine map. Chaos is found in the systems, and complexity of the systems is controlled by the parameter of the memristor. Finally, FPGA digital circuit implementation is carried out for the integer-order and fractional-order discrete memristor and discrete memristive systems, which shows the potential application value of the discrete memristor in the engineering application field

    Gene Expression Network Reconstruction by LEP Method Using Microarray Data

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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
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