Orbital stability of periodic traveling wave solutions to the generalized zakharov equations

Zheng, Xiaoxiao; Shang, Yadong; Peng, Xiaoming

doi:10.1016/s0252-9602(17)30054-1

Cited by 41 publications

(25 citation statements)

References 17 publications

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“…It is known that stability is an important research topic in the mathematical field [1][2][3][4][5][6][7][8][9][10][11][12][13]. As a special class of mathematical models, neural networks are similar to the brain synapses link structure; neural networks possess multiple dynamic behaviors [14].…”

Section: Introductionmentioning

confidence: 99%

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

Yogambigai

Ali

Zhu

et al. 2018

Mathematical Problems in Engineering

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The problem of exponential Lagrange stability analysis of Markovian jump neural networks with leakage delay and mixed timevarying delays is studied in this paper. By utilizing the Lyapunov functional method, employing free-weighting matrix approach and inequality techniques in matrix form, we establish several novel stability criteria such that, for all admissible parameter uncertainties, the suggested neural network is exponentially stable in Lagrange sense. The derived criteria are expressed in terms of linear matrix inequalities (LMIs). A numerical example is provided to manifest the validity of the proposed results.

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Section: Introductionmentioning

confidence: 99%

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

Yogambigai

Ali

Zhu

et al. 2018

Mathematical Problems in Engineering

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show abstract

“…There are many papers about BAM neural networks and stochastic BAM neural networks; for details, see [13][14][15][16][17][18]. It is known that the existence-uniqueness and stability is an important theoretical problem in the field of dynamics systems and one can find this topic in these papers [19][20][21][22]. Always, leakage delays appear in the negative feedback term of neural networks.…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability of Antiperiodic Solution for BAM Neural Networks with Time-Varying Delays

Qin

Zhu

2018

Mathematical Problems in Engineering

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In this paper, a kind of BAM neural networks with leakage delays in the negative feedback terms and time-varying delays in activation functions was considered. By constructing a suitable Lyapunov function and using inequality techniques, some sufficient conditions to ensure the existence and exponential stability of antiperiodic solutions of these neural networks were derived. These conditions extend some results recently appearing in recent papers. Lastly, an example is given to show the feasibility of these conditions.

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“…Descriptor system theory is an important part in control systems theory. Since 1970s, descriptor systems have been wildly studied, for example, descriptor linear systems [1], descriptor nonlinear systems [2][3][4], and discrete descriptor systems [5][6][7]. In particular, Dai has systematically introduced the theoretical basis of descriptor systems in [8], which is the first monograph on this subject.…”

Section: Introductionmentioning

confidence: 99%

A New Sufficient Condition for Checking the Robust Stabilization of Uncertain Descriptor Fractional-Order Systems

Wang

Liu

2018

Journal of Function Spaces

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We consider the robust asymptotical stabilization of uncertain a class of descriptor fractional-order systems. In the state matrix, we require that the parameter uncertainties are time-invariant and norm-bounded. We derive a sufficient condition for the system with the fractional-order satisfying 1 ≤ < 2 in terms of linear matrix inequalities (LMIs). The condition of the proposed stability criterion for fractional-order system is easy to be verified. An illustrative example is given to show that our result is effective.

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Orbital stability of periodic traveling wave solutions to the generalized zakharov equations

Cited by 41 publications

References 17 publications

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

Exponential Stability of Antiperiodic Solution for BAM Neural Networks with Time-Varying Delays

A New Sufficient Condition for Checking the Robust Stabilization of Uncertain Descriptor Fractional-Order Systems

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