A memristive map with coexisting chaos and hyperchaos*

Kong, Sixiao; Li, Chunbiao; He, Shaobo; Çiçek, Serdar; Lai, Qiang

doi:10.1088/1674-1056/abf4fb

Cited by 43 publications

(15 citation statements)

References 55 publications

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“…[8][9][10][11][12][13] As a fourth circuit element with natural non-linearity and plasticity, memristors can easily be combined with chaotic system circuits to construct chaotic systems based on memristors. [14][15][16][17][18][19][20][21][22] Currently, chaotic systems have been used in a wide range of applications such as neural network chaotic systems, [23][24][25][26][27][28][29][30][31][32] secure communications, [33][34][35][36][37] synchronization, [38][39][40] PRNG, [41][42][43][44] image encryption, [45][46][47][48][49][50][51][52][53] and fractional-order chaotic system. [54][55]…”

Section: Introductionmentioning

confidence: 99%

FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient

Zhang

Shen

et al. 2022

Chinese Phys. B

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In this paper, a memristive Hopfield neural network with a special activation gradient (MHNN) is proposed by adding a suitable memristor to the Hopfield neural network (HNN) with a special activation gradient. The MHNN is simulated and dynamic analyzed, and implemented on FPGA. Then, a new pseudo-random number generator (PRNG) based on MHNN is proposed. The post-processing unit of the PRNG is composed of nonlinear post-processor and XOR calculator, which effectively ensures the randomness of PRNG. The experiments in this paper comply with the IEEE 754-1985 high precision 32-bit floating point standard and are done on the Vivado design tool using a Xilinx XC7Z020CLG400-2 FPGA chip and the Verilog-HDL hardware programming language. The random sequence generated by the PRNG proposed in this paper has passed the NIST SP800-22 test suite and security analysis, proving its randomness and high performance. Finally, an image encryption system based on PRNG is proposed and implemented on FPGA, which proves the value of the image encryption system in the field of data encryption connected to the Internet of Things (IoT).

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Section: Introductionmentioning

confidence: 99%

FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient

Zhang

Shen

et al. 2022

Chinese Phys. B

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“…[3] Very recently, discrete memristor has begun to receive many researchers' attention. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] For instance, Peng et al presented a model of discrete memristor via the difference theory and derived a memristive Hénon map in Ref. [4].…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [14], Kong et al put forward a 2D memristive map by introducing a discrete sinusoidal memristor. Liu gave and investigated a memristive map by couping the discrete memristor with nonlinear maps of sine and cosine functions in Ref.…”

Section: Introductionmentioning

confidence: 99%

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

et al. 2022

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In this work, we present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are demonstrated and investigated using different numerical tools, including phase portrait, basins of attraction, bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map has been carried out to reveal the bifurcation mechanism of the dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors. They can exhibit extremely hidden multi-stability, namely the coexistence of infinite hidden attractors, rarely shown in memristive maps. Potentially, this work can be used for secure communication, such as data and image encryption.

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“…And it avoids the disadvantage that parameter sensitivity of the continuous nonlinear system, so the discrete system is more concerned in the practical engineering. Inspired by the mathematical model of the continuous memristor, the discussion of discrete memristor becomes a topical issue in recently [20][21][22][23][24][25][26]. He and Peng et al proposed the integer-order and fractional-order discrete memristor mathematical models, and introduced these discrete models into the sine map [20] and two high-dimensional chaotic maps [21,22].…”

Section: Introductionmentioning

confidence: 99%

Parameter identification for discrete memristive chaotic map using adaptive differential evolution algorithm

Peng

Sun

2021

Nonlinear Dyn

Self Cite

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Since the concept of discrete memristor was proposed, more and more scholars began to study this topic. At present, most of the works on the discrete memristor are devoted to the mathematical modeling and circuit implementation, but the research on its synchronization control has not received much attention. This paper focuses on the parameter identification for the discrete memristive chaotic map, and a modified intelligent optimization algorithm named adaptive differential evolution algorithm is proposed. To deal with the complex behaviors of hyperchaos and coexisting attractors of the considered discrete memristive chaotic maps, the identification objective function adopts two special parts: time sequences and return maps. Numerical simulations demonstrate that the proposed algorithm has the best performance among the six existing algorithms, and it can still accurately identify the parameters of the original system under noise interference.

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A memristive map with coexisting chaos and hyperchaos*

Cited by 43 publications

References 55 publications

FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient

FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

Parameter identification for discrete memristive chaotic map using adaptive differential evolution algorithm

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