Complex bursting patterns and fast-slow analysis in a smallest chemical reaction system with two slow parametric excitations

Zhou, Chengyi; Xie, Fei; Li, Zhijun

doi:10.1016/j.chaos.2020.109859

Cited by 35 publications

(5 citation statements)

References 30 publications

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“…As a consequence, many chaotic systems possessing abundant dynamical behaviors have been investigated in recent years. [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.…”

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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“…Bursting dynamics [1,2], also called mixed-mode oscillations [3,4] or relaxation vibrations [5,6], created by the multi-time scale effect [7,8], is often observed in many nonlinear models, such as circuit oscillators [9,10], mechanical systems [11,12], nervous models [13,14] and chemical reactions [15,16]. Bursting oscillation is a complex dynamical behavior consisting of comparatively big-amplitude waves and approximately simple harmonic micro-amplitude vibrations, and is universally studied with the help of the slow/fast decomposition analysis that is proposed by in Rinzel [17] in 1985.…”

Section: Introductionmentioning

confidence: 99%

Intermittent bursting oscillations and the bifurcation analysis in an excited Rayleigh-Duffing oscillator

Zhang

Tang

Wang

2022

Preprint

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This paper investigates the bursting oscillations of a externally and parametrically forced Rayleigh-Duffing oscillator, in which three intermittent bursting types and one normal bursting type, namely intermittent “supHopf/supHopf-supHopf/supHopf” bursting, intermittent “fold/Homoclinic-Homoclinic/supHopf” bursting, intermittent “fold/Homoclinic-supHopf/supHopf” bursting and “fold/Homoclinic” bursting, are analyzed respectively. Recognizing the excitations as slow-varying state variables, the corresponding autonomous system can be exhibited and the bifurcation characteristics is briefly investigated, in particular, the Homoclinic bifurcation is analyzed by means of the Melnikov criterion. This paper shows that the dynamical behaviors of the excited Rayleigh-Duffing oscillator is touchy to the chosen of system parameters, different parameter conditions lead to distinct bifurcation structures that result in the trajectory approaching to different stable attractors and the appearance of different bursting forms. Our study increases the variousness of bursting oscillations and deepens the cognition of the generation mechanism of bursting dynamics. Lastly, the accuracy of the analysis presented in this paper is fully vindicated by the numerical simulations.

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“…Because the first simple three-dimensional chaotic system has been proposed by Lorenz (1963), scientists have discovered the great application of the chaos systems in secure communication (Li et al , 2020; Wang et al , 2020; Yu et al , 2020a; Lin et al , 2021a), image encryption (Xu et al , 2020a; Cheng et al , 2020; Xu et al , 2020b; Zeng and Wang, 2021; Deng et al , 2021) and neural network (Lin et al , 2020a; Lin et al , 2020b; Lin et al , 2020c; Lin et al , 2020d; Yao et al , 2020). To meet the needs of engineering applications, researchers are committed to construct chaotic systems with more dynamic behaviors such as transient chaos (Xie et al , 2021), hyperchaos (Yu et al , 2021; Wu et al , 2018; Feng et al , 2017), coexisting attractors (Lai et al , 2019; Pham et al , 2017a; Lai and Chen, 2017) and bursting dynamics (Zhou et al , 2020; Wen et al , 2020; Wen et al , 2019; Lin et al , 2021b). It is widely recognized that equilibrium points of a chaotic system play important roles in chaos theory.…”

Section: Introductionmentioning

confidence: 99%

Hidden multiwing chaotic attractors with multiple stable equilibrium points

Deng

Wang

et al. 2022

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Purpose The purpose of this paper is to construct a multiwing chaotic system that has hidden attractors with multiple stable equilibrium points. Because the multiwing hidden attractors chaotic systems are safer and have more dynamic behaviors, it is necessary to construct such a system to meet the needs of developing engineering. Design/methodology/approach By introducing a multilevel pulse function into a three-dimensional chaotic system with two stable node–foci equilibrium points, a hidden multiwing attractor with multiple stable equilibrium points can be generated. The switching behavior of a hidden four-wing attractor is studied by phase portraits and time series. The dynamical properties of the multiwing attractor are analyzed via the Poincaré map, Lyapunov exponent spectrum and bifurcation diagram. Furthermore, the hardware experiment of the proposed four-wing hidden attractors was carried out. Findings Not only unstable equilibrium points can produce multiwing attractors but stable node–foci equilibrium points can also produce multiwing attractors. And this system can obtain 2N + 2-wing attractors as the stage pulse of the multilevel pulse function is N. Moreover, the hardware experiment matches the simulation results well. Originality/value This paper constructs a new multiwing chaotic system by enlarging the number of stable node–foci equilibrium points. In addition, it is a nonautonomous system that is more suitable for practical projects. And the hardware experiment is also given in this article which has not been seen before. So, this paper promotes the development of hidden multiwing chaotic attractors in nonautonomous systems and makes sense for applications.

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Complex bursting patterns and fast-slow analysis in a smallest chemical reaction system with two slow parametric excitations

Cited by 35 publications

References 30 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

Intermittent bursting oscillations and the bifurcation analysis in an excited Rayleigh-Duffing oscillator

Hidden multiwing chaotic attractors with multiple stable equilibrium points

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