Về việc sử dụng phương pháp quang phổ bậc cao và tiến trình hình học để phân tích sự phân nhánh tĩnh của các bài toán phi tuyến

International Journal of Dynamics and Control - Tập 11 - Trang 2633-2643 - 2023
Mohamed Drissi1, Said Mesmoudi2, Mohamed Mansouri1
1LAMSAD Laboratory, Ecole National des Sciences Appliqués, Hassan First University of Settat, Berrechid, Morocco
2LISA Laboratory, Ecole National des Sciences Appliqués, Hassan First University of Settat, Berrechid, Morocco

Tóm tắt

Trong nghiên cứu này, chúng tôi đề xuất việc sử dụng kỹ thuật tiến trình hình học vô hình bậc cao màu đỏ để khám phá định lượng các điểm phân nhánh ổn định và các nhánh phân nhánh. Chúng tôi đề xuất sử dụng phương pháp bậc cao (HOA) để giải quyết các bài toán phi tuyến. Phương pháp đề xuất kết hợp kỹ thuật tiếp tục tiệm cận và một phép phân rã được thực hiện bằng phương pháp quang phổ bậc hai. Các phương trình điều khiển được trình bày dưới dạng một cấu trúc phi tuyến mạnh mẽ. Các phương trình phi tuyến được chuyển đổi thành một chuỗi các phương trình tuyến tính nhờ vào phương pháp vô hình bậc cao (HOA). Phương pháp này cho phép phát hiện chính xác vị trí phân nhánh. Một chiến lược giải quyết nhằm xử lý các sự kiện phân nhánh cho các bài toán biharmonic bằng cách mở rộng trong các hình học khác nhau, trong đó vấn đề ổn định trở thành không ổn định sau một điểm tới hạn. Các phát hiện thu được được so sánh với những gì đã được báo cáo trong tài liệu và với những gì được tính toán bằng phương pháp phần tử hữu hạn bậc cao kết hợp với tiến trình hình học.

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