Control of Multistability in a Self-Excited Memristive Hyperchaotic Oscillator

Fozin, T. Fonzin; Kengne, Romanic; Kengne, Jacques; Srinivasan, K.; Tagueu, M. Souffo; Pelap, F. B.

doi:10.1142/s0218127419501190

Cited by 32 publications

(20 citation statements)

References 49 publications

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“…In order to confirm the results obtained previously, this section focused on the implementation of the controlled HNN using PSPICE simulations software [ 13 , 14 , 18 , 29 , 30 , 48 ]. Remark that the hardware experiments on a breadboard would have been welcome.…”

Section: Circuit Implementationmentioning

confidence: 81%

“…The implementation of this control method of linear augmentation consists to couple a linear dynamic system with a nonlinear system and then increasing the coupling strength in order to achieve the control goal, which can be described as [ 45 – 48 ] …”

Section: Theory Of Linear Augmentationmentioning

confidence: 99%

“…The circuit in Fig. 10 has been designed following the method of analog computer-based on Miller integrators, using operational amplifiers, capacitors, resistors [ 13 , 14 , 18 , 29 , 30 , 48 ]. The neuron state variables and the controller state variable of Eq.…”

Section: Circuit Implementationmentioning

confidence: 99%

“…Since its solid successful application prior in 2011 on the stabilization of fixed-point solution in chaotic systems by Sharma et al [ 46 ], the linear augmentation scheme has been extended later on the control of bistability in chaotic attractors comprising of well-separated unstable steady state [ 47 ]. In addition, Fozin et al [ 48 ] have exploited this technic on linear augmentation to control the coexistence of three attractors in a hyperchaotic system. However, from these aforementioned works, there is no one focused on the control of multistability in a dynamical system with up to four or more than four attractors.…”

Section: Introductionmentioning

confidence: 99%

“…It is important to stress that the linear augmentation method has been considered in the literature only to control two different attractors (i.e., bistable or tristable systems) [ 48 ]. Also to the best of authors’ knowledge, no other chaotic systems, particularly no HNN with up to six disconnected stable states, have been successfully controlled in the literature until date.…”

Section: Introductionmentioning

confidence: 99%

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Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Njitacke

Doubla

Tsafack

et al. 2020

Neural Comput & Applic

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In this contribution, the problem of multistability control in a simple model of 3D HNNs as well as its application to biomedical image encryption is addressed. The space magnetization is justified by the coexistence of up to six disconnected attractors including both chaotic and periodic. The linear augmentation method is successfully applied to control the multistable HNNs into a monostable network. The control of the coexisting four attractors including a pair of chaotic attractors and a pair of periodic attractors is made through three crises that enable the chaotic attractors to be metamorphosed in a monostable periodic attractor. Also, the control of six coexisting attractors (with two pairs of chaotic attractors and a pair of periodic one) is made through five crises enabling all the chaotic attractors to be metamorphosed in a monostable periodic attractor. Note that this controlled HNN is obtained for higher values of the coupling strength. These interesting results are obtained using nonlinear analysis tools such as the phase portraits, bifurcations diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The obtained results have been perfectly supported using the PSPICE simulation environment. Finally, a simple encryption scheme is designed jointly using the sequences of the proposed HNNs and the sequences of real/imaginary values of the Julia fractals set. The obtained cryptosystem is validated using some well-known metrics. The proposed method achieved entropy of 7.9992, NPCR of 99.6299, and encryption time of 0.21 for the 256*256 sample 1 image.

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Section: Circuit Implementationmentioning

confidence: 81%

Section: Theory Of Linear Augmentationmentioning

confidence: 99%

Section: Circuit Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Njitacke

Doubla

Tsafack

et al. 2020

Neural Comput & Applic

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Image encryption using a novel quintic jerk circuit with adjustable symmetry

Kengne

Nkandeu

Pone

et al. 2021

Circuit Theory & Apps

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Summary An electronic implementation of a novel chaotic oscillator with quintic nonlinearity is proposed herein. Dynamical behaviors of the system are investigated using well‐known numerical simulations and analyses such as phase portraits, Lyapunov exponents, bifurcation diagrams, and basins of attraction. The chaotic circuit presents an inversion‐symmetry, and we show that it can exhibit some nonlinear phenomena specific to symmetric systems, such as symmetric bifurcations, symmetric attractors, coexisting symmetric bubbles, and coexisting symmetric attractors. Since symmetry is never perfect, some symmetry imperfections must be always assumed to be present. Thus, an external Direct Current (DC) voltage is introduced in order to highlight the influence of asymmetry on the dynamics of the chaotic oscillator. It is found that more complex nonlinear behaviors occur in the presence of symmetry breaking like asymmetric coexisting bifurcations, asymmetric attractors, coexisting asymmetric bubbles, and coexisting asymmetric attractors, to name a few. The control of multistability is also performed by using the so‐called linear augmentation scheme. Probe Simulation Program with Integrated Circuits Emphasis (Pspice) circuit simulations are carried out to verify the theoretical analyses. Furthermore, a chaos‐based image encryption is investigated using pseudorandom numbers generated by the proposed chaotic circuit and deoxyribonucleic acid (DNA) encoding technique.

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A coupling method of double memristors and analysis of extreme transient behavior

Liu

Zhang

et al. 2021

Nonlinear Dyn

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Control of Multistability in a Self-Excited Memristive Hyperchaotic Oscillator

Cited by 32 publications

References 49 publications

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption

Image encryption using a novel quintic jerk circuit with adjustable symmetry

A coupling method of double memristors and analysis of extreme transient behavior

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