Uncertain destination dynamics of a novel memristive 4D autonomous system

Njitacke, Zeric Tabekoueng; Kengne, Jacques; Tapche, R. Wafo; Pelap, F. B.

doi:10.1016/j.chaos.2018.01.004

Cited by 75 publications

(25 citation statements)

References 26 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: 82%

“…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%

“…In this scope, there are special cases of multistability which have attracted much attention in recent years. Among others, we have systems with extreme multistability (characterized by the coexistence of an infinite number of attractors, in this case, the bifurcation control parameter is one of the initial conditions) [ 27 – 30 ]. Other types of multistable systems found recently are systems with megastability [ 31 – 35 ].…”

Section: Introductionmentioning

confidence: 99%

See 2 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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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: 82%

Section: Circuit Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

show abstract

“…Multistability is an interesting phenomenon connected with nonlinear dynamics, meaning the coexistence of two or more attractors in the phase space, for a kept fixed set of parameters present in the related mathematical model. Coexisting attractors may be of the same type (stable equilibrium point, periodic, quasiperiodic, or chaotic) or not, having been detected in several different discreteand continuous-time systems, modeled by different sets of mathematical equations [8][9][10][11][12][13][14][15]. Therefore, multistability is a typical phenomenon of nonlinear dynamical systems that arises as a consequence of its sensitive dependence on initial conditions.…”

Section: Multistability In the Forced Brusselatormentioning

confidence: 99%

Multistability in a Periodically Forced Brusselator

Rech

2020

Braz J Phys

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In this paper, we report on multistability in a periodically forced Brusselator, which is modeled by a nonlinear nonautonomous system of two first-order ordinary differential equations. Multistability regions are detected in a cross section of the four-dimensional parameter space of the model, namely the (ω, F) parameter plane, where ω and F are respectively angular frequency and amplitude of an external forcing. Lyapunov exponents spectra are used to characterize the dynamical behavior of each point in the abovementioned parameter plane. Moreover, basins of attraction, bifurcation diagrams, and phase-space portraits are used to illustrate the coexistence of periodic and chaotic behaviors.

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“…Particularly, memristive systems based on ideal memristors can produce the extreme multistability phenomenon of coexisting infinitely many attractors [22,23]. Such a special phenomenon is commonly triggered in the systems with no equilibrium [24] or infinitely many equilibria [16,[25][26][27][28], entirely different from those generated from the offset-boostable flow by introducing an extra periodic 2 Complexity signal [29][30][31]. In [17], a memristor-based Colpitts chaotic oscillator was proposed by introducing a nonideal extended memristor into original Colpitts oscillator [2].…”

Section: Introductionmentioning

confidence: 99%

Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor‐Based Colpitts System

et al. 2019

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In this paper, a four-dimensional (4-D) memristor-based Colpitts system is reaped by employing an ideal memristor to substitute the exponential nonlinear term of original three-dimensional (3-D) Colpitts oscillator model, from which the initials-dependent extreme multistability is exhibited by phase portraits and local basins of attraction. To explore dynamical mechanism, an equivalent 3-D dimensionality reduction model is built using the state variable mapping (SVM) method, which allows the implicit initials of the 4-D memristor-based Colpitts system to be changed into the corresponding explicitly initials-related system parameters of the 3-D dimensionality reduction model. The initials-related equilibria of the 3-D dimensionality reduction model are derived and their initials-related stabilities are discussed, upon which the dynamical mechanism is quantitatively explored. Furthermore, the initials-dependent extreme multistability is depicted by two-parameter plots and the coexistence of infinitely many attractors is demonstrated by phase portraits, which is confirmed by PSIM circuit simulations based on a physical circuit.

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Uncertain destination dynamics of a novel memristive 4D autonomous system

Cited by 75 publications

References 26 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

Multistability in a Periodically Forced Brusselator

Dimensionality Reduction Reconstitution for Extreme Multistability in Memristor‐Based Colpitts System

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