Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

Boya, Bertrand Frederick Boui A; Kengne, Jacques; Kenmoé, G. Djuidjé; Effa, Joseph Yves

doi:10.1016/j.heliyon.2022.e11046

Cited by 13 publications

(6 citation statements)

References 32 publications

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“…This language is very closed and compatible with the C programming language. Here digital components replace analog circuits as the latter is influenced by the temperature of the components, atmospheric conditions, and pressure [ 31 , 32 , 33 , 34 , 35 ], to name just a few. Based on the microcontroller implementation in described in Ref.…”

Section: Experimental Investigationmentioning

confidence: 99%

Effects of bias current and control of multistability in 3D hopfield neural network

Boya

Ramakrishnan²,

Effa

et al. 2023

Heliyon

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Section: Experimental Investigationmentioning

confidence: 99%

Effects of bias current and control of multistability in 3D hopfield neural network

Boya

Ramakrishnan²,

Effa

et al. 2023

Heliyon

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“…Experimental validation of the coupled Hopfield inertial neurons is relevant to confirm numerical analysis and useful for engineering applications; which means that the theoretical systems can be constructed and manufactured in real life [12,14,19]. Here, we set some parameters, and the experimental results based on microcontroller implementation of the Coupled Hopfield inertial neurons are shown in figure 11.…”

Section: Microcontroller-based Experimentsmentioning

confidence: 99%

“…In computational neuroscience, therefore, several research studies have been carried out to improve our knowledge to the electrical activity of coupled neurons models [3] [3][4][5]. As a result, several phenomena were observed in those works, including firing activity [6,7], multi-scroll dynamics [8][9][10], and multistability [11][12][13]. The design of simple chaotic models with complex chaotic orbits and multiple coexistence of attractors is still a hot topic in nonlinear dynamics area [14,15].…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Madasamy,

Boui a Boya,

Kengne

et al. 2023

Phys. Scr.

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This work deals with the regular and chaotic dynamics of a system made up of two Hopfield-type neurons with two different activation functions: the hyperbolic tangent function and the Crespi function. The mathematical model is in the form of an autonomous differential system of order four with odd symmetry. The analysis highlights nine equilibrium points and four of these points experience a Hopf bifurcation at the same critical value of a control parameter which can be either the diss1ipation parameter or one of the coupling coefficients. This makes plausible the presence of four parallel bifurcation branches as well as the coexistence of multiple attractors in the behavior of the system. One of the highlights revealed in this work is the coexistence of three double-scroll type attractors of particular topology as well as the presence of a four-spiral attractor. Furthermore, the coexistence of both self-excited and hidden dynamics is also reported. All this plethora of dynamics is elucidated by making use of the usual tools for analyzing nonlinear systems such as bifurcation diagrams, the maximum of Lyapunov exponent, basins of attractions as well as phase portraits. A physical implementation of the microcontroller-based system is envisaged in order to confirm the plethora of behaviors observed theoretically.

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“…This section aims to look for some analogies between the experimental results and those obtained previously in order to validate the numerical results. The microcontroller-based implementation offers great flexibility and facilitates the experimental detection of the dynamics of complex systems [40][41][42][43][44][45]. It is for this reason that we have produced the microcontroller implementation whose diagram is in the figure 16 which mimics system dynamics (4).…”

Section: Implementation Electronique Of Modified Helmholtz Jerk Oscil...mentioning

confidence: 99%

Nonlinear dynamics, coexistence of attractors and microcontroller implementation of a modified Helmholtz Jerk oscillator

Fangnon¹,

Tamba²,

Miwadinou

et al. 2023

Phys. Scr.

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In this work, we converted a two-dimensional modiﬁed Helmholtz oscillator into a three-dimensional modiﬁed Helmholtz jerk oscillator. The study of the stability of the ﬁxed points is made and by using the theorem of Hopf, the condition of existence of the bifurcation of Hopf is sought. By numerical simulations relating to the diagrams of the basin of parameters, attraction, bifurcation, the Lyapunov exponents and the phase portrait, the global dynamics as well as the coexistence of the attractors of the system are analyzed. This study revealed that the considered modiﬁed Jerk Helmholtz oscillator can generate Hopf bifurcation, bistable limit cycles, coexistence of chaotic and periodic attractors for appropriate choices of system parameter values. The microcontroller based implementation of the modiﬁed Jerk Helmholtz oscillator is proposed to experimentally verify the obtained analytical and numerical results. Finally, to control the amplitude of the Lyapunov attractor and exponent, we added two new parameters in the modiﬁed Helmholtz jerk oscillator.

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Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

Cited by 13 publications

References 32 publications

Effects of bias current and control of multistability in 3D hopfield neural network

Effects of bias current and control of multistability in 3D hopfield neural network

Collective dynamics of two coupled Hopfield inertial neurons with different activation functions: theoretical study and microcontroller implementation

Nonlinear dynamics, coexistence of attractors and microcontroller implementation of a modified Helmholtz Jerk oscillator

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