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Sự phân nhánh Hopf toàn cầu của mô hình động vật ăn thịt và con mồi Leslie–Gower sửa đổi có khuếch tán với độ trễ và thu hoạch con mồi loại Michaelis–Menten
Tóm tắt
Trong bài báo này, chúng tôi nghiên cứu sự phân nhánh Hopf toàn cầu của một mô hình động vật ăn thịt và con mồi Leslie–Gower sửa đổi có khuếch tán với độ trễ và thu hoạch con mồi loại Michaelis–Menten. Đầu tiên, chúng tôi xác định được tính ổn định của trạng thái ổn định dương và sự tồn tại của phân nhánh Hopf cục bộ dưới các điều kiện nhất định. Thứ hai, chúng tôi đạt được tính ổn định vĩnh cửu của hệ thống bằng cách sử dụng định lý so sánh. Hơn nữa, bằng cách xây dựng một hàm Lyapunov phù hợp, chúng tôi đưa ra các điều kiện đủ cho tính hấp dẫn toàn cầu của trạng thái ổn định dương duy nhất của hệ thống không có độ trễ. Sau đó, sự tồn tại toàn cầu của các nghiệm tuần hoàn dương được thiết lập bằng cách sử dụng kết quả phân nhánh Hopf toàn cầu của Wu. Cuối cùng, các kết quả này được xác minh bằng mô phỏng số.
Từ khóa
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