Piecewise asymptotic almost periodic solutions for impulsive fuzzy Cohen–Grossberg neural networks

Abdelaziz, Meryem; Chérif, Farouk

doi:10.1016/j.chaos.2019.109575

Cited by 23 publications

(6 citation statements)

References 26 publications

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“…It is well known that neural networks have been applied in various areas such as image processing, optimization, artificial intelligence, computer version, automatic control and so on [1,17]. Thus the study on various dynamical behaviors of neural networks is an interesting and important topic in today's world.…”

Section: Introductionmentioning

confidence: 99%

“…have been reported. For example, Abdelaziz and Chérif [1] discussed the piecewise asymptotic almost periodic solutions of fuzzy Cohen-Grossberg neural networks. Aouiti et al [2] detailedly analyzed the piecewise pseudo almost periodic solution to delayed neutral-type neural networks.…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 presents some elementary knowledge on fractional calculus and integer-order differential equations. Section 3 is concerned with the discussion on the stability and the emergence of Hopf bifurcation of the integerorder delayed BAM neural networks (1). Section 4 deals with the analysis on the stability and the emergence of Hopf bifurcation of the fractional-order delayed BAM neural networks (2).…”

Section: Introductionmentioning

confidence: 99%

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Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

Liu

et al. 2022

NAMC

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In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

Liu

et al. 2022

NAMC

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“…In the recent years, there were many efforts in designing hybrid structures where neural networks were combined with the concept of fuzzy logic to suppress individual drawbacks and emphasize their advantages [18,19]. For instance, fuzzy Cohen-Grossberg neural networks [20,21], one type of cellular neural networks, have been extensively studied due to their wide applications in classification, pattern recognition, parallel computing, and image processing. These hybrid structures usually integrate fuzzy logic into the structure of neural network by replacing single steps of the inference process by different layers of the neural network.…”

Section: Introductionmentioning

confidence: 99%

Designing optimal models of nonlinear MIMO systems based on orthogonal polynomial neural networks

Milojković

Milovanović

Nikolić

et al. 2021

Mathematical and Computer Modelling of Dynamical Systems

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This paper presents a new method for modelling of dynamic systems by using specially designed orthogonal polynomial neural networks. These networks utilize the feature that the basis made of orthogonal functions can be used for approximation of arbitrary function, while their property of orthogonality enables optimal performances in the sense of both convergence time and approximation error. In this regard, generalized quasi-orthogonal polynomials, specifically tailored for the application in the modelling of complex dynamic systems with time-varying behaviour, are considered. Adaptivity of the designed model is achieved by using variable factors inside the orthogonal basis. The designed orthogonal neural network is applied in modelling of laboratory twin-rotor aero-dynamic system as a representative of nonlinear multiple input-multiple output systems. Detailed comparative analysis is performed for a different number of polynomials in expansion with the purpose of finding the optimal model in the sense of tradeoff between model accuracy and complexity.

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“…In 2019, Huang et al [7] set up a sufficient criterion to guarantee the existence of anti-periodic solutions and exponential stability for shunting inhibitory cellular neural networks involving proportional time delays by applying Lyapunov functional, inequality shills, and some mathematical analyses. In 2020, Abdelaziz and Chérif [8] carried out the study on the piecewise asymptotic almost periodic solutions of fuzzy Cohen-Grossberg neural networks involving impulsive effect. Xu and Li [9] did a valuable and novel work on anti-periodic solution to delayed cellular neural networks involving D operator.…”

Section: Introductionmentioning

confidence: 99%

New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

Tang

2021

Journal of Mathematics

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In the current work, we are devoted to the issue of uniform stability of fractional-order quaternion-valued neural networks involving discrete and leakage delays. Making use of the contracting mapping theory, we prove that the equilibrium point of the involved fractional-order quaternion-valued neural networks exists and is unique. Taking advantage of mathematical analysis strategy, a sufficient criterion involving delay to verify the global uniform stability for the considered fractional-order quaternion-valued neural networks is set up. Computer simulation figures are displayed to sustain the rationality of the established conclusions. This study generalizes and supplements the research of Xiu et al. (2020).

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Piecewise asymptotic almost periodic solutions for impulsive fuzzy Cohen–Grossberg neural networks

Cited by 23 publications

References 26 publications

Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

Designing optimal models of nonlinear MIMO systems based on orthogonal polynomial neural networks

New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

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