状態依存スイッチングを有する区分的線形活性化関数付きCVNNの多安定性解析と連想記憶への応用

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 [Formula: see text] equilibrium points, among which [Formula: see text] 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.