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<p>This paper investigates the multistability of complex-valued neural networks (CVNNs) with state-dependent switching rules and discontinuous nonmonotonic piecewise linear activation functions featuring <i>k</i> peaks. By leveraging Brouwer’s fixed point theorem and the properties of strictly diagonally dominant matrices, we analyze the existence, stability, and instability of equilibrium points through state space decomposition. Our results demonstrate that an <i>n</i>-neuron switching CVNNs can possess up to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((2k+5) ^{2n}\)</EquationSource> </InlineEquation> equilibrium points, among which <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((k+3) ^{2n}\)</EquationSource> </InlineEquation> are stable. These findings significantly extend existing results and enrich the stability theory of neural networks. Numerical examples validate the theoretical conclusions and illustrate potential applications in associative memory.</p>

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Multistability analysis of state-dependent switching CVNNs with discontinuous nonmonotonic piecewise linear activation function and its application in associative memory

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Weiqiang Gong,
  • Liu Yang,
  • Qiang Li,
  • Zeyuan Huang,
  • Linzhong Zhang,
  • Feifei Du

摘要

This paper investigates the multistability of complex-valued neural networks (CVNNs) with state-dependent switching rules and discontinuous nonmonotonic piecewise linear activation functions featuring k peaks. By leveraging Brouwer’s fixed point theorem and the properties of strictly diagonally dominant matrices, we analyze the existence, stability, and instability of equilibrium points through state space decomposition. Our results demonstrate that an n-neuron switching CVNNs can possess up to \((2k+5) ^{2n}\) equilibrium points, among which \((k+3) ^{2n}\) are stable. These findings significantly extend existing results and enrich the stability theory of neural networks. Numerical examples validate the theoretical conclusions and illustrate potential applications in associative memory.