Design and FPGA Implementation of a Pseudorandom Number Generator Based on a Four-Wing Memristive Hyperchaotic System and Bernoulli Map

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Novel memristive hyperchaotic system designs and their engineering applications have received considerable critical attention. In this paper, a novel multistable 5D memristive hyperchaotic system and its application are introduced. The interesting aspect of this chaotic system is that it has different types of coexisting attractors, chaos, hyperchaos, periods, and limit cycles. First, a novel 5D memristive hyperchaotic system is proposed by introducing a flux-controlled memristor with quadratic nonlinearity into an existing 4D four-wing chaotic system as a feedback term. Then, the phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy are used to analyze the basic dynamics of the 5D memristive hyperchaotic system. For a specific set of parameters, we find an unusual metastability, which shows the transition from chaotic to periodic (period-2 and period-3) dynamics. Moreover, its circuit implementation is also proposed. By using the chaoticity of the novel hyperchaotic system, we have developed a random number generator (RNG) for practical image encryption applications. Furthermore, security analyses are carried out with the RNG and image encryption designs.

Section: Introductionmentioning

confidence: 99%

Chaos-Based Application of a Novel Multistable 5D Memristive Hyperchaotic System with Coexisting Multiple Attractors

Liu

Qian

et al. 2020

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“…In other words, assuming that the current state in diagnoser G d is q 1 d , while the next observable event is σ, we generate the new state q 2 d of G d in the following way: (1) For each (q o , l) ∈ q 1 d , compute the set S(q o , σ) of reachable states of G from q o using observation σ:…”

Section: Classical Diagnoser For Dessmentioning

confidence: 99%

“…is F-incomparable, according to Lemma A.1-(ii), there exist two strings s, s ′ ∈ L with s e , s e ′ ∈ Σ o such that l 1 1…”

Section: Appendixmentioning

confidence: 99%

“…Nonlinear science is a new interdisciplinary subject which studies the common problems proposed by nonlinear interaction widely existing in various disciplines, especially in complex networks [1][2][3][4], system control [5][6][7], secure communication [8][9][10], chaotic systems [11], random number generators [12,13], discrete-event systems (DESs) [14], and other fields. e creative work on the diagnosis/ diagnosability of DESs, presented in [15,16], with the originally proposed concept of a diagnoser, model-based diagnosis, and diagnosability have attracted more and more attention, as indicated by the large number of methods and techniques proposed in the literature, including [17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Minimal Diagnosis and Diagnosability of Discrete-Event Systems Modeled by Automata

Zhao

Lamperti

Ouyang³

et al. 2020

In the last several decades, the model-based diagnosis of discrete-event systems (DESs) has increasingly become an active research topic in both control engineering and artificial intelligence. However, in contrast with the widely applied minimal diagnosis of static systems, in most approaches to the diagnosis of DESs, all possible candidate diagnoses are computed, including nonminimal candidates, which may cause intractable complexity when the number of nonminimal diagnoses is very large. According to the principle of parsimony and the principle of joint-probability distribution, generally, the minimal diagnosis of DESs is preferable to a nonminimal diagnosis. To generate more likely diagnoses, the notion of the minimal diagnosis of DESs is presented, which is supported by a minimal diagnoser for the generation of minimal diagnoses. Moreover, to either strongly or weakly decide whether a minimal set of faulty events has definitely occurred or not, two notions of minimal diagnosability are proposed. Necessary and sufficient conditions for determining the minimal diagnosability of DESs are proven. The relationships between the two types of minimal diagnosability and the classical diagnosability are analysed in depth.

“…With the rapid development of computer technology, the accompanying information security issues have attracted more and more attention and become a hot issue [32][33][34][35][36][37][38][39][40][41][42]. Chaos is widely used in cryptosystems, random numbers, and secure communications [43][44][45][46][47][48][49], and it has become a hot topic in nonlinear circuits and systems. In the realization of chaotic circuits, researchers have proposed many new methods to design different types of chaotic circuits [50][51][52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

CCII and FPGA Realization: A Multistable Modified Fourth-Order Autonomous Chua’s Chaotic System with Coexisting Multiple Attractors

Shen

Liu

et al. 2020

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In this paper, a multistable modified fourth-order autonomous Chua’s chaotic system is investigated. In addition to the dynamic characteristics of the third-order Chua’s chaotic system itself, what interests us is that this modified fourth-order autonomous Chua’s chaotic system has five different types of coexisting attractors: double-scroll, single band chaotic attractor, period-4 limit cycle, period-2 limit cycle, and period-1 limit cycle. Then, an inductorless modified fourth-order autonomous Chua’s chaotic circuit is proposed. The active elements as well as the synthetic inductor employed in this circuit are designed using second-generation current conveyors (CCIIs). The reason for using CCIIs is that they have high conversion rate and operation speed, which enable the circuit to work at a higher frequency range. The Multisim simulations confirm the theoretical estimates of the performance of the proposed circuit. Finally, using RK-4 numerical algorithm of VHDL 32-bit IQ-Math floating-point number format, the inductorless modified fourth-order autonomous Chua’s chaotic system is implemented on FPGA for the development of embedded engineering applications based on chaos. The system is simulated and synthesized on Virtex-6 FPGA chip. The maximum operating frequency of modified Chua’s chaotic oscillator based on FPGA is 180.180 MHz. This study demonstrates that the hardware-based multistable modified fourth-order autonomous Chua’s chaotic system is a very good source of entropy and can be applied to various embedded systems based on chaos, including secure communication, cryptography, and random number generator.