| 石仁祥.带有常时滞循环耦合神经网络的全局指数稳定性[J].,2017,57(5):537-544 |
| 带有常时滞循环耦合神经网络的全局指数稳定性 |
| Global exponential stability of cycle associative neural network with constant delays |
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| DOI：10.7511/dllgxb201705015 |
| 中文关键词: 指数稳定性 平衡点 神经网络 Lyapunov函数 |
| 英文关键词: exponential stability equilibrium point neural network Lyapunov function |
| 基金项目:江苏省自然科学基金资助项目(BK20131285). |
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| 中文摘要: |
| 讨论了带有常时滞循环耦合神经网络的全局指数稳定性 在讨论过程中通过构造同胚映射论证了该系统平衡点的存在性与唯一性 再通过构造合适的Lyapunov函数论证唯一平衡点是全局指数稳定的 类似于已有的神经网络稳定性方面工作 在神经元的激励函数满足Lipschitz条件且相关系数构成矩阵也满足给定条件下 得到 n 层带有常时滞的神经网络全局指数稳定的动力学性质 所得结果同时也蕴含当神经元的衰减速率足够大时 神经网络是全局指数稳定的 |
| 英文摘要: |
| The global exponential stability of cycle associative neural network with constant delays is discussed. During the discussion, by constructing homeomorphism mapping, it is demonstrated that there exists an equilibrium point which is unique for this system, then the global exponential stability of the unique equilibrium point is testified by constructing proper Lyapunov function. Similar to previous work about neural network stability, under the assumption that the activation function about neuron satisfies Lipschitz condition and the matrix constructed by correlation coefficient satisfies given condition, the dynamics of global exponential stability for n -layer neural network with constant delays are obtained. The results contain that when the passive rate of neuron is sufficiently large, the neural network is global exponential stable. |
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