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<p>The generalized stability and associative memory of delayed recurrent neural networks with variable external inputs are investigated in this paper. Based on the comparison principle, the monostability of normal differentiable systems is established, which is extended to neural networks with variable external inputs. Furthermore, the coexistence of multiple equilibrium points in delayed recurrent neural networks is analyzed, and the number of stable equilibrium points is increased by extending the activation functions to enhance storage capacity. Several sufficient conditions are then derived to ensure the generalized stability of these equilibrium points, which extends and encompasses the classical concept of exponential stability. Moreover, an associative memory with high capacity is designed based on stable bipolar patterns with freely chosen components. Finally, the theoretical results and the design of associative memory are verified by two numerical examples.</p>

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Generalized stability and associative memory of delayed recurrent neural networks with variable external input

  • 期刊论文

  • 发表日期：

    2025年8月19日

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  • Fanghai Zhang,
  • Peng Gao,
  • Tingwen Huang,
  • Zhigang Zeng

摘要

The generalized stability and associative memory of delayed recurrent neural networks with variable external inputs are investigated in this paper. Based on the comparison principle, the monostability of normal differentiable systems is established, which is extended to neural networks with variable external inputs. Furthermore, the coexistence of multiple equilibrium points in delayed recurrent neural networks is analyzed, and the number of stable equilibrium points is increased by extending the activation functions to enhance storage capacity. Several sufficient conditions are then derived to ensure the generalized stability of these equilibrium points, which extends and encompasses the classical concept of exponential stability. Moreover, an associative memory with high capacity is designed based on stable bipolar patterns with freely chosen components. Finally, the theoretical results and the design of associative memory are verified by two numerical examples.