Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Xây Dựng Các Giải Phương Trình Gần Chu Kỳ Của Các Phương Trình Vi Đạo Hạn Chế Thời Gian Phụ Thuộc Trạng Thái Bằng Phương Pháp Tham Số Hóa I: Trường Hợp Siêu Đẳng Khuếch Tán, Nguồn Khả Diện
Tóm tắt
Trong bài báo này, chúng tôi sử dụng phương pháp tham số hóa để xây dựng các giải pháp gần chu kỳ cho các phương trình vi đạo có độ trễ phụ thuộc vào trạng thái. Ví dụ
$$\begin{aligned} \left\{ \begin{aligned} \dot{x}(t)&=f(\theta ,x(t),\epsilon x(t-\tau (x(t))))\\ \dot{\theta }(t)&=\omega . \end{aligned} \right. \end{aligned}$$
Dưới giả thuyết về phân tách mũ cho trường hợp $$\epsilon =0$$, chúng tôi sử dụng lập luận ánh xạ co để chứng minh sự tồn tại và độ mịn của giải pháp gần chu kỳ. Hơn nữa, kết quả được trình bày dưới định dạng a posteriori. Phương pháp này rất tổng quát và cũng áp dụng cho các phương trình có nhiều độ trễ, độ trễ phân bố, v.v.
Từ khóa
#phương trình vi đạo #độ trễ phụ thuộc trạng thái #giải pháp gần chu kỳ #phương pháp tham số hóa #ánh xạ coTài liệu tham khảo
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