几类神经网络模型的动力学分析
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摘要
本文探讨了几类神经网络的动力学行为。首先，我们给出了离散型细胞神经网络存在全局吸引的概周期序列解和κ-概周期序列解的新结果。我们的结果是基于神经网络的参数，不仅容易验证而且能为神经网络在实际应用中的实时计算提供出相应的数值估计。我们还进一步发展了适用于具有分段常数项微分方程的wa(?)ewski类型拓扑方法，并利用它来研究具有分段常数项神经网络解的定性行为。其次，通过利用Laypunov泛函和不等式技巧我们给出了具有非线性脉冲的双向联想记忆神经网络平衡点的存在性和全局指数型稳定性。此外，我们还探讨了具有有限分布时滞的脉冲双向联想记忆神经网络指数型周期吸引子的动力学行为。最后，我们研究了Cohen-Grossberg神经网络的一些动力学特性。通过利用Laypunov-Krasovskii泛函和同胚映射原理，我们得到了具有传输时滞和Hebbian类型学习行为的二阶Cohen-Grossberg神经网络平衡点稳定性的一些结果。我们的结果不仅给出了平衡点的全局指数型p-稳定，还给出了神经元在学习过程中的指数型收敛行为。对于具有分布时滞的脉冲Cohen-Grossberg神经网络，我们给出平衡点稳定性的充分条件不仅容易验证，而且我们不需要行为函数的可逆性和激活函数的有界性。我们的结果适用于一般Cohen-Grossberg神经网络的应用和设计。
In this thesis, we investigate dynamic behaviors of several classes of neural networks. First, we derive new criteria for the existence and global attractivity of almost periodic sequence solution and k-almost periodic sequence solution of discrete-time cellular neural networks. These criteria based on system parameters are easy for us to check. Our results can also provide us with relevant estimates on how precise such networks can perform during real-time computations in applications. Furthermore, we develop a topological approach of wa(z|·)ewski-type which is suitable for differential equations with piecewise constant argument to investigate qualitative behavior of cellular neural networks with piecewise constant argument. Secondly, by using Laypunov-Krasovskii functional and inequality technique, some sufficient conditions for the existence and global stability of equilibrium are attained for bidirectional associative memory (BAM) neural networks with nonlinear impulses. The exponential stability of periodic solutions for BAM neural networks with finite distributed delays is also discussed. At last, we discuss dynamical properties of Cohen-Grossberg neural networks. By using Laypunov-Krasovskii functional and homeomorphism mapping, some new sufficient conditions are established for global exponential p-stability of a unique equilibrium for second order Cohen-Grossberg neural networks with transmission delays and an unsupervised Hebbian-type learning behavior. Moreover, the learning dynamic behavior of neurons is also given. For impulsive Cohen-Grossberg networks with distributed delays, the obtained results of stability of equilibrium are easy to verify, meanwhile we remove the boundedness of activation functions and invertibility of the suitable behaved functions. It is believed that these results are suitable and useful for the design and applications of general Cohen-Grossberg networks.
In this thesis, we investigate dynamic behaviors of several classes of neural networks. First, we derive new criteria for the existence and global attractivity of almost periodic sequence solution and k-almost periodic sequence solution of discrete-time cellular neural networks. These criteria based on system parameters are easy for us to check. Our results can also provide us with relevant estimates on how precise such networks can perform during real-time computations in applications. Furthermore, we develop a topological approach of wa(z|·)ewski-type which is suitable for differential equations with piecewise constant argument to investigate qualitative behavior of cellular neural networks with piecewise constant argument. Secondly, by using Laypunov-Krasovskii functional and inequality technique, some sufficient conditions for the existence and global stability of equilibrium are attained for bidirectional associative memory (BAM) neural networks with nonlinear impulses. The exponential stability of periodic solutions for BAM neural networks with finite distributed delays is also discussed. At last, we discuss dynamical properties of Cohen-Grossberg neural networks. By using Laypunov-Krasovskii functional and homeomorphism mapping, some new sufficient conditions are established for global exponential p-stability of a unique equilibrium for second order Cohen-Grossberg neural networks with transmission delays and an unsupervised Hebbian-type learning behavior. Moreover, the learning dynamic behavior of neurons is also given. For impulsive Cohen-Grossberg networks with distributed delays, the obtained results of stability of equilibrium are easy to verify, meanwhile we remove the boundedness of activation functions and invertibility of the suitable behaved functions. It is believed that these results are suitable and useful for the design and applications of general Cohen-Grossberg networks.
引文
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