Global stability analysis of fractional-order fuzzy BAM neural networks with time delay and impulsive effects

Ali, M. Syed; Narayanan, G.; Sevgen, Selçuk; Shekher, Vineet; Arik, Sabri

doi:10.1016/j.cnsns.2019.104853

Cited by 49 publications

(22 citation statements)

References 55 publications

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“…[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] With the development of fractional calculus, lots of scholars have found that fractional calculus can be widely applied in various areas such as neural networks, computer science, electromagnetic waves, biotechnology, mechanics, and control engineering. [31][32][33][34] Compared with the conventional integer-order case, the fractional calculus acts as a very effective tool to depict memory and hereditary of various materials and dynamical process in object world. [31][32][33][34] In recent several decades, the fractional-order differential systems have received great attention.…”

Section: Introductionmentioning

confidence: 99%

“…[31][32][33][34] Compared with the conventional integer-order case, the fractional calculus acts as a very effective tool to depict memory and hereditary of various materials and dynamical process in object world. [31][32][33][34] In recent several decades, the fractional-order differential systems have received great attention. In particular, the research on fractional-order neural networks has attracted widespread interest of many scholars.…”

Section: Introductionmentioning

confidence: 99%

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Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Aouiti

2020

Circuit Theory & Apps

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Summary This article mainly focuses on the stability and the existence of Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. First of all, we obtain the sufficient criterion to ensure the stability and the existence of Hopf bifurcation of integer‐order two‐neuron neural networks with delay. Next, we establish the sufficient condition guaranteeing the stability and the existence of Hopf bifurcation of fractional‐order two‐neuron neural networks with delay. The study reveals that the time delay has a vital effect on the stability and Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay. By comparative analysis on Hopf bifurcation for integer‐order and fractional‐order two‐neuron neural networks with delay, we find that under an appropriate parameter conditions, the stability region can be enlarged, and the time of appearance of Hopf bifurcation of the involved two‐neuron neural networks can be postponed by using fractional‐order case. Finally, computer simulation results are presented to illustrate the theoretical findings. The established results of this article play an important role in designing and controlling networks.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Aouiti

2020

Circuit Theory & Apps

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“…The other is discontinuous, and can help with control issues like impulses. Impulsive control technique has attracted attention of many researchers, due to its applications in finance, biological models and medicine [33][34][35]. It is a discontinuous control method and many advantages compared to continuous control (statefeedback control) techniques such as high reliability, efficiency, easy installation, and low cost maintenance.…”

Section: Introductionmentioning

confidence: 99%

Quasi‐bipartite synchronisation of multiple inertial signed delayed neural networks under distributed event‐triggered impulsive control strategy

Udhayakumar

Rihan

et al. 2021

IET Control Theory & Appl

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The central concern of this paper is to study leader-following quasi-bipartite synchronisation of a multiple inertial signed neural networks with varying time-delay by utilising distributed event-triggered impulsive control scheme, where connections between adjacent nodes of the neural networks either positive or negative. The second-order neural networks, called inertial neural networks, can be transformed into differential equations of first-order by implementing suitable variable substitution. Under certain hypothesis about the node dynamics, signed graph theory and balanced topology of networks, some conditions are derived in terms of lower-dimensional linear matrix inequalities (LMIs) to achieve leader-following quasi-bipartite synchronisation. In addition, a basic algebraic condition is derived to estimate the theoretical upper bound for the error node. Finally, some numerical simulations are provided to illustrate the correctness of the theoretical results.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…In several areas, such as electrical circuit analysis, finance insurance, dynamic systems, computing, and physical field, third-order difference equations appeared to scrutinize discrete models, naturally occurring in discrete models pertaining physical, biological, and chemical phenomena (see, for example, [1][2][3][4][5][6][7][8]). In many engineering problems, analyzing the existence of oscillatory solutions performs an essential role.…”

Section: Introductionmentioning

confidence: 99%

Qualitative Property of Third-Order Nonlinear Neutral Distributed-Delay Generalized Difference Equations

Sumathy¹,

Reddy²,

Manuel³

2021

Mathematical Problems in Engineering

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Global stability analysis of fractional-order fuzzy BAM neural networks with time delay and impulsive effects

Cited by 49 publications

References 55 publications

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

Quasi‐bipartite synchronisation of multiple inertial signed delayed neural networks under distributed event‐triggered impulsive control strategy

Qualitative Property of Third-Order Nonlinear Neutral Distributed-Delay Generalized Difference Equations

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