Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks

Hu, Haijun; Yuan, Xupu; Huang, Lihong; Huang, Chuangxia

doi:10.3934/mbe.2019286

Cited by 71 publications

(27 citation statements)

References 39 publications

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“…Remark To the author's knowledge, the issue of antiperiodic RNNs involving proportional delays has never been investigated. Obviously, the corresponding conclusions in Shao, Tan, Gong, Cao, Li, Zhou, Yang, Wang, Peng and Wang, Cai et al, Li et al, Kudu, Hu et al, Hu and Zou, Huang et al, and Hu et al and the references cited therein cannot be used to deal with the exponential convergence on the

π

antiperiodic phenomenon for system .…”

Section: Numerical Example and Simulationsmentioning

confidence: 99%

Stability of antiperiodic recurrent neural networks with multiproportional delays

Huang

Long

Cao

2020

Math Methods in App Sciences

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In general, a proportional function is obviously not antiperiodic, yet a very interesting fact in this paper shows that it is possible there is an antiperiodic solution for some proportional delayed dynamical systems. We deal with the issue of antiperiodic solutions for RNNs (recurrent neural networks) incorporating multiproportional delays. Employing Lyapunov method, inequality techniques and concise mathematical analysis proof, sufficient criteria on the existence of antiperiodic solutions including its uniqueness and exponential stability are built up. The obtained results provide us some lights for designing a stable RNNs and complement some earlier publications. In addition, simulations show that the theoretical antiperiodic dynamics are in excellent agreement with the numerically observed behavior. KEYWORDSantiperiodic, proportional delay, recurrent neural network, stability MSC CLASSIFICATION 34C25; 34K13; 34K25Math Meth Appl Sci. 2020;43:6093-6102.wileyonlinelibrary.com/journal/mma

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π

antiperiodic phenomenon for system .…”

Section: Numerical Example and Simulationsmentioning

confidence: 99%

Stability of antiperiodic recurrent neural networks with multiproportional delays

Huang

Long

Cao

2020

Math Methods in App Sciences

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“…We know that the next state of a system depends not only upon its current state but also upon its historical information. In addition to the classical delay differential equation modeling, fractional calculus is also a pretty effective tool to describe the nonlocal and weakly singular kernel . As usual, there are two advantages in models of fractional order: One is allowing more degree of freedom in the models, and the other is describing memory properties in the models.…”

Section: Introductionmentioning

confidence: 99%

Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

Anbalagan

Raja

Alzabut

et al. 2020

Math Methods in App Sciences

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Fractional order quaternion‐valued neural networks are a type of fractional order neural networks for which neuron state, synaptic connection strengths, and neuron activation functions are quaternion. This paper is dealing with the Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. The fractional order quaternion‐valued neural networks are separated into four real‐valued systems forming an equivalent four real‐valued fractional order neural networks, which decreases the computational complexity by avoiding the noncommutativity of quaternion multiplication. Via some fractional inequality techniques and suitable Lyapunov functional, a brand new criterion is proposed first to ensure the Mittag‐Leffler stability for the addressed neural networks. Besides, the combination of quaternion‐valued adaptive and impulsive control is intended to realize the asymptotically synchronization between two fractional order quaternion‐valued neural networks. Ultimately, two numerical simulations are provided to check the accuracy and validity of our obtained theoretical results.

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“…In recent times, differential equation and fractional differential equation models have found their applications in a variety of fields including biology [1][2][3][4][5][6], physics [7][8][9][10], engineering [11][12][13][14], mathematics [15][16][17][18], information technology, and so on [19][20][21][22][23][24][25][26][27]. They are also one of the most rudimentary tools for neural networks.…”

Section: Introduction and Modelingmentioning

confidence: 99%

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

et al. 2020

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In this research work, the finite-time synchronization and adaptive finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks (FCDNNs) are investigated under two different control strategies. By utilizing differential inclusion theory, Filippov framework, suitable Lyapunov functional, and graph theory approach, several sufficient criteria based on discontinuous state feedback control protocol and discontinuous adaptive feedback control protocol are established for ensuring the finite-time synchronization and adaptive finite-time synchronization of FCDNNs. Finally, two numerical cases illustrate the efficiency of the proposed finite-time synchronization results.

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Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks

Cited by 71 publications

References 39 publications

Stability of antiperiodic recurrent neural networks with multiproportional delays

Stability of antiperiodic recurrent neural networks with multiproportional delays

Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

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