In this work, we introduce a simple method to investigate the asymptotic stability of discrete dynamical systems, which can be considered as an extension of the classical Lyapunov’s indirect method. This method is constructed based on the classical Lyapunov’s indirect method and the idea proposed by Ghaffari and Lasemi in a recent work. The new method can be applicable even when equilibia of dynamical systems are non-hyperbolic. Hence, in many cases, the classical Lyapunov’s indirect method fails but the new one can be used simply. In addition, by combining the new stability method with the Mickens’ methodology, we formulate some nonstandard finite difference (NSFD) methods which are able to preserve the asymptotic stability of some classes of differential equation models even when they have non-hyperbolic equilibrium points. As an important consequence, some well-known results on stabilitypreserving NSFD schemes for autonomous dynamical systems are improved and extended. Finally, a set of numerical examples are performed to illustrate and support the theoretical findings
Bài báo quốc tế
Kho tri thức
/
Bài báo quốc tế
/
A simple method for studying asymptotic stability of discrete dynamical systems and its applications
A simple method for studying asymptotic stability of discrete dynamical systems and its applications
Hoàng Mạnh Tuấn, Ngô Thị Kim Quy, Trương Hà Hải
Xuất bản trên:
International Journal of Optimization and Control: Theories & Applications
Ngày đăng:
2023
Nhà xuất bản:
Địa điểm:
Từ khoá:
Discrete dynamical systems, Lyapunov’s indirect method, Asymptotic stability, Non-hyperbolic equilibrium point, Nonstandard finite difference methods
Bài báo liên quan
A survey on the Impact of Hyperparameters on Random Forest performance using multiple accelerometer datasets
Lê Hồng Lam, Lê Thành Tươi, Vũ Thị Thu Hiền, Trần Đoàn Hiếu, Đinh Văn Châu, Ngô Thị Thu TrangMachine Learning approaches for Stem Cells
Mazlee Mazalan, Wan Safwani Wan Kamarul Zaman, Effỉrul Ramlan, Đỗ Tiến DũngLevitin-Polyak Well-posedness for Symmetric Weak Vector Quasi-equilibrium Problems
Jen Chih Yao, Nguyen Huynh Vu Duy, Elisabeth Kobis, Nguyễn Văn HưngLearning Adaptive Quantization Parameter for Consistent Quality Oriented Video Coding
Phí Công Huy, Hoàng Văn Xiêm, Đỗ Ngọc Minh, Nguyễn Quang Sang, Thipphaphone Sisouvong, Vũ Hữu Tiến