Existence and Uniqueness of Solutions for Cohen–Grossberg BAM Neural Networks with Time-Varying Leakage, Neutral, Distributed, and Transmission Delays

Er-Yong Cong (), Xian Zhang () and Li Zhu
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Er-Yong Cong: Department of Mathematics, Harbin University, Harbin 150086, China
Xian Zhang: School of Mathematical Science, Heilongjiang University, Harbin 150080, China
Li Zhu: Department of Mathematics, Harbin University, Harbin 150086, China

Mathematics, 2025, vol. 13, issue 17, 1-14

Abstract: This paper establishes a rigorous theoretical framework for analyzing the existence and uniqueness of solutions to Cohen–Grossberg bidirectional associative memory neural networks (CGBAMNNs) incorporating four distinct types of time-varying delays: leakage, neutral, distributed, and transmission delays. This study makes three key contributions to the field: First, it overcomes the fundamental challenge posed by the system’s inherent inability to be expressed in vector–matrix form, which previously limited the application of standard analytical techniques. Second, the work develops a novel and generalizable methodology that not only proves sufficient conditions for solution existence and uniqueness but also, for the first time in the literature, provides an explicit representation of the unique solution. Third, the proposed framework demonstrates remarkable extensibility, requiring only minor modifications to be applicable to a wide range of delayed system models. Theoretical findings are conclusively validated through numerical simulations, confirming both the robustness of the proposed approach and its practical relevance for complex neural network analysis.

Keywords: Cohen–Grossberg BAM neural networks; existence and uniqueness of solution; time-varying leakage; distributed delays (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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