Dynamic stability analysis of stochastic fractional-order memristor fuzzy BAM neural networks with delay and leakage terms

Ali, M. Syed; Narayanan, G.; Shekher, Vineet; Alsulami, Hamed; Saeed, Tareq

doi:10.1016/j.amc.2019.124896

Cited by 42 publications

(17 citation statements)

References 56 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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“…"Novel results on bifurcation for fractional-order complex-valued neural networks with leakage delay" were established in [43]. Lastly, the "dynamic stability of stochastic delayed fractional-order memristor-based fuzzy BAM neural networks with leakage delay" was studied in [44].…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

Popa

Kaslik

2020

Mathematics

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This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.

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“…ere are many research studies on fractional-order BAM neural networks [6][7][8][9][10][11]. A novel result about finite-time impulsive stability of fractional-order memristive BAM neural networks is obtained in [6].…”

Section: Introductionmentioning

confidence: 99%

“…In [10], sufficient conditions for the existence, uniqueness, and global Mittag-Leffler stability for the solutions of the fractional difference model of BAM neural networks are provided. In [11], based on Cauchy-Schwartz inequality and Burkholder-Davis-Gundy inequality, some sufficient conditions are derived to ensure the uniform stability of stochastic fractional-order memristor fuzzy BAM neural networks. e definitions of Mittag-Leffler stability and generalized Mittag-Leffler stability are proposed in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

Yan

Qiao

Duan

et al. 2020

Mathematical Problems in Engineering

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In this paper, the global Mittag–Leffler stabilization of fractional-order BAM neural networks is investigated. First, a new lemma is proposed by using basic inequality to broaden the selection of Lyapunov function. Second, linear state feedback control strategies are designed to induce the stability of fractional-order BAM neural networks. Third, based on constructed Lyapunov function, generalized Gronwall-like inequality, and control strategies, several sufficient conditions for the global Mittag–Leffler stabilization of fractional-order BAM neural networks are established. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

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Dynamic stability analysis of stochastic fractional-order memristor fuzzy BAM neural networks with delay and leakage terms

Cited by 42 publications

References 56 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

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

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