Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

Ling, Zhou; Wang, Chunhua; Xin, Zhang; Yao, Wei

doi:10.1142/s0218127418500505

Cited by 93 publications

(40 citation statements)

References 39 publications

(52 reference statements)

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“…For chaotic systems, hidden attractors [42][43][44][45][46] and infinite attractors [47][48][49][50] can exhibit multistability. For example, complex dynamic behaviors of coexisting attractors [51], transient chaos [52], and limit cycle [53] can be observed from hidden attractors. Recently, various multistable memristive hyperchaotic systems have been proposed in many literatures.…”

Section: Introductionmentioning

confidence: 99%

Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

Zhang

Liu

et al. 2020

Complexity

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By introducing a flux-controlled memristor model with absolute value function, a 5D multistable four-wing memristive hyperchaotic system (FWMHS) with linear equilibrium points is proposed in this paper. The dynamic characteristics of the system are studied in terms of equilibrium point, perpetual point, bifurcation diagram, Lyapunov exponential spectrum, phase portraits, and spectral entropy. This system is of the group of systems that have coexisting attractors. In addition, the circuit implementation scheme is also proposed. Then, a secure communication scheme based on the proposed 5D multistable FWMHS with disturbance inputs is designed. Based on parametric modulation theory and Lyapunov stability theory, synchronization and secure communication between the transmitter and receiver are realized and two message signals are recovered by a convenient robust high-order sliding mode adaptive controller. Through the proposed adaptive controller, the unknown parameters can be identified accurately, the gain of the receiver system can be adjusted continuously, and the disturbance inputs of the transmitter and receiver can be suppressed effectively. Thereafter, the convergence of the proposed scheme is proven by means of an appropriate Lyapunov functional and the effectiveness of the theoretical results is testified via numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

Zhang

Liu

et al. 2020

Complexity

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“…Since 1960, the research and application of nonlinear systems have been more and more extensive. Many problems in complex networks [1][2][3][4][5][6][7], memristor [8][9][10][11], electronic circuits [12][13][14][15], image processing [16][17][18][19][20][21], economics [22], and other fields can be attributed to the study of nonlinear systems. Chaos is a special state of motion in a nonlinear system, which is a random-like behavior generated by a deterministic system and is extremely sensitive to initial values and highly dependent on them [23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

“…Many analog implementations of chaotic systems in electronic circuits have been reported in recent decades, such as the well-known breadboard with discrete components [10,13,27,28] and CMOS technology for integrated circuit (IC) design [12,23,24]. However, breadboard is not easy to carry, maintain, and store data, and IC design has a long cycle and high cost [83][84][85][86][87].…”

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

Complexity

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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.

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“…The application of mem-elements to chaotic circuits is an important research topic. Some different memristor emulators have been proposed and applied to different chaotic circuits to generate various chaotic phenomena, [11][12][13][14][15][33][34][35][36][37][38][39] Indeed, simulation analyses show that not only memristor but also memcapacitor and meminductor can be used to construct chaotic oscillator. Recently, many researchers proposed some new memcapacitor and meminductor models and designed chaotic oscillators based on the proposed models.…”

Section: Introductionmentioning

confidence: 99%

A universal emulator for memristor, memcapacitor, and meminductor and its chaotic circuit

Zhao

Wang

Zhang

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

167

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In this paper, a universal charge-controlled mem-elements (including memristor, memcapacitor, and meminductor) emulator consisting of off-the-shelf devices is proposed. With the unchanged topology of the circuit, the emulator can realize memristor, memcapacitor, and meminductor, respectively. The proposed emulation circuit has a simple mathematical relationship and is constructed with few active devices and passive components, which not only reduces the cost but also facilitates reproduction and facilitates future application research. The grounding and floating forms of the circuit are demonstrated, and Multisim circuit simulation and breadboard experiments validate the emulator's effectiveness. Furthermore, a universal mem-elements chaotic circuit is designed by using the proposed mem-elements emulator and other circuit elements, which is a deformation circuit of Chua's dual circuit. In this circuit, no matter whether the mem-element is memristor, memcapacitor, or meminductor, the chaotic circuit structure does not change, and all can generate hyper-chaos.

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Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

Cited by 93 publications

References 39 publications

Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs

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

A universal emulator for memristor, memcapacitor, and meminductor and its chaotic circuit

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