Sự tồn tại và tiêu chí ổn định tiệm cận toàn cục cho mạng nơ-ron loại trung tính phi tuyến với nhiều độ trễ thời gian sử dụng hàm Lyapunov tích phân bậc hai

Springer Science and Business Media LLC - Tập 2021 - Trang 1-26 - 2021
Yousef Gholami1
1Department of Applied Mathematics, Sahand University of Technology, Tabriz, Iran

Tóm tắt

Trong bài báo này, chúng tôi xem xét một lớp tiêu chuẩn của các mạng nơ-ron và đề xuất một cuộc điều tra về sự ổn định tiệm cận toàn cục của các hệ thống nơ-ron này. Mục tiêu chính của cuộc điều tra này là định nghĩa một hàm Lyapunov mới có dạng tích phân bậc hai và sử dụng nó để đạt được một tiêu chí ổn định cho các mạng nơ-ron đang được nghiên cứu. Vì một số đặc điểm cơ bản, chẳng hạn như phi tuyến, bao gồm độ trễ thời gian và tính trung tính, giúp chúng tôi thiết kế một mô hình của các hệ thống nơ-ron thực tế và khả thi hơn, chúng tôi sẽ sử dụng tất cả các yếu tố này trong các hệ thống động học nơ-ron của mình. Cuối cùng, một số mô phỏng số được trình bày để minh họa tiêu chí ổn định thu được và cho thấy vai trò thiết yếu của độ trễ thời gian trong sự xuất hiện của dao động và sự ổn định trong các mạng nơ-ron.

Từ khóa

#mạng nơ-ron #ổn định tiệm cận toàn cục #hàm Lyapunov #độ trễ thời gian #mô hình phi tuyến

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