Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

Yao, Wei; Wang, Chunhua; Sun, Yichuang; Zhou, Chao; Lin, Hairong

doi:10.1016/j.amc.2020.125483

Cited by 40 publications

(33 citation statements)

References 56 publications

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“…In addition, fractional calculus has the memory characteristic with respect to time. Memristor is the fourth fundamental circuit element [2] which is widely used in chaotic neural networks [3][4][5][6], circuit design [7][8][9], secure communications [10][11][12], bio-simulation circuit [13] and logic circuit [14]. Memristor has the same memory characteristic as fractional calculus, so memristor can be extended to fractional-order.…”

Section: Introductionmentioning

confidence: 99%

A fractional-order multistable locally active memristor and its chaotic system with transient transition, state jump

2021

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Fractional calculus is closer to reality and has the same memory characteristics as memristor. Therefore, a fractional-order multistable locally active memristor is proposed for the first time in this paper, which has infinitely many coexisting pinched hysteresis loops under different initial states and wide locally active regions. Through the theoretical and numerical analysis, it is found that the fractional-order memristor has stronger locally active and memory characteristics and wider nonvolatile ranges than the integer-order memristor. Furthermore, this fractional-order memristor is applied in a chaotic system. It is found that oscillations occur only within the locally active regions. This chaotic system not only has complex and rich nonlinear dynamics such as infinitely many discrete equilibrium points, multistability, anti-monotonicity but also produces two new phenomena that have not been found in other chaotic systems after neglecting some initial transients. The first one is transient transition: the behavior of transient chaotic and transient period transition alternately occurring. The second is state jump: the behavior of period-4 oscillation or chaotic oscillation jumping to period-2 oscillation. Finally, the circuit simulation of the fractional-order multistable locally active memristive chaotic system using PSIM is carried out to verify the validity of the numerical simulation results.

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Section: Introductionmentioning

confidence: 99%

A fractional-order multistable locally active memristor and its chaotic system with transient transition, state jump

2021

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“…How to construct a good PRNG and generate high-performance and high-quality PRNs has always been a hot topic for scholars. Chaos is widely used in complex networks [13][14][15][16], electronic circuits [17][18][19][20], image encryption [21][22][23][24][25], synchronous control [26][27][28], encryption system [29][30][31][32], and other fields because of its good random characteristics, extreme sensitivity to initial values and parameters, longterm unpredictability, and ergodicity of orbits. e PRNs based on the chaos system have the advantages of fast generation speed, high security performance, and good statistical characteristics.…”

Section: Introductionmentioning

confidence: 99%

Chaos‐Based Engineering Applications with a 6D Memristive Multistable Hyperchaotic System and a 2D SF‐SIMM Hyperchaotic Map

Qian

Chen

et al. 2021

Complexity

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In recent years, the research of chaos theory has developed from simple cognition and analysis to practical engineering application. In particular, hyperchaotic systems with more complex and changeable chaotic characteristics are more sensitive and unpredictable, so they are widely used in more fields. In this paper, two important engineering applications based on hyperchaos pseudorandom number generator (PRNG) and image encryption are studied. Firstly, the coupling 6D memristive hyperchaotic system and a 2D SF-SIMM discrete hyperchaotic mapping are used as the double entropy source structure. The double entropy source structure can realize a new PRNG that meets the security requirements, which can pass the NIST statistical test when the XOR postprocessing method is used. Secondly, based on the double entropy source structure, a new image encryption algorithm is proposed. The algorithm uses the diffusion-scrambling-diffusion encryption scheme to realize the conversion from the original plaintext image to the ciphertext image. Finally, we analyze the security of the proposed PRNG and image encryption mechanism, respectively. The results show that the proposed PRNG has good statistical output characteristics and the proposed image encryption scheme has high security, so they can be effectively applied in the field of information security and encryption system.

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“…Recently, chaotic systems have attracted wide attention from researchers due to their own particularities and their vast application potential in the memristor [1][2][3][4], random number generator [5,6], secure communication [7][8][9], image encryption [10][11][12][13][14], and artificial neural network [15][16][17][18][19][20]. How to increase the complexity of a chaotic system and generate complex chaotic attractors to make it hard to encipher information in encryption system applications has become a field of interest for researchers both in and outside China.…”

Section: Introductionmentioning

confidence: 99%

Basin of Attraction Analysis of New Memristor‐Based Fractional‐Order Chaotic System

Ding

Cui

2021

Complexity

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Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

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Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

Cited by 40 publications

References 56 publications

A fractional-order multistable locally active memristor and its chaotic system with transient transition, state jump

A fractional-order multistable locally active memristor and its chaotic system with transient transition, state jump

Chaos‐Based Engineering Applications with a 6D Memristive Multistable Hyperchaotic System and a 2D SF‐SIMM Hyperchaotic Map

Basin of Attraction Analysis of New Memristor‐Based Fractional‐Order Chaotic System

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