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Existence of Exponential p‐Stability Nonconstant Equilibrium of Markovian Jumping Nonlinear Diffusion Equations via Ekeland Variational Principle

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  • Ruofeng Rao
  • Shouming Zhong

Abstract

The authors obtained a delay‐dependent exponential p‐stability criterion for a class of Markovian jumping nonlinear diffusion equations by employing the Lyapunov stability theory and some variational methods. As far as we know, it is the first time to apply Ekeland variational principle to obtain the existence of exponential stability equilibrium of p‐Laplacian dynamic system so that some methods used in this paper are different from those methods of many previous related literatures. In addition, the obtained existence criterion is only involved in the activation functions so that the criterion is simpler and easier than other existence criteria to be verified in practical application. Moreover, a numerical example shows the effectiveness of the proposed methods owing to the large allowable variation range of time‐delay.

Suggested Citation

  • Ruofeng Rao & Shouming Zhong, 2015. "Existence of Exponential p‐Stability Nonconstant Equilibrium of Markovian Jumping Nonlinear Diffusion Equations via Ekeland Variational Principle," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:812150
    DOI: 10.1155/2015/812150
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    References listed on IDEAS

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    1. Xiongrui Wang & Ruofeng Rao & Shouming Zhong, 2012. "LMI Approach to Stability Analysis of Cohen‐Grossberg Neural Networks with p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Chen, Hao & Zhong, Shouming & Shao, Jinliang, 2015. "Exponential stability criterion for interval neural networks with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 121-130.
    3. Pan Qingfei & Zhang Zifang & Huang Jingchang, 2012. "Stability of the Stochastic Reaction‐Diffusion Neural Network with Time‐Varying Delays and p‐Laplacian," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Pan Qingfei & Zhang Zifang & Huang Jingchang, 2012. "Stability of the Stochastic Reaction-Diffusion Neural Network with Time-Varying Delays and p -Laplacian," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, December.
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