Modeling and Dynamic Analysis of Algae–Fish Model with Two State-Dependent Impulse Controls
Abstract
:1. Introduction
2. State Feedback Impulsive Model
2.1. Free Developing Model
2.2. State Feedback Impulsive Model
3. Analysis of Continuous System Dynamic Behavior
- (1)
- If , then is the stable node point.
- (2)
- If , then is the degenerate node point.
- (3)
- If , then is the stable focus point.
4. Existence and Stability of Periodic Solution
4.1. Existence and Stability of Order-1 Periodic Solution
4.2. Existence and Stability of Order-2 Periodic Solution
5. Numerical Simulation
5.1. The Order-1 Periodic Solution Numerical Simulation
5.2. The Order-2 Periodic Solution Numerical Simulation
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Liu, Y.; Zhuang, Y.; Liu, Q.; Huang, L. Modeling and Dynamic Analysis of Algae–Fish Model with Two State-Dependent Impulse Controls. Symmetry 2024, 16, 1265. https://doi.org/10.3390/sym16101265
Liu Y, Zhuang Y, Liu Q, Huang L. Modeling and Dynamic Analysis of Algae–Fish Model with Two State-Dependent Impulse Controls. Symmetry. 2024; 16(10):1265. https://doi.org/10.3390/sym16101265
Chicago/Turabian StyleLiu, Ying, Yuan Zhuang, Qiong Liu, and Lizhuang Huang. 2024. "Modeling and Dynamic Analysis of Algae–Fish Model with Two State-Dependent Impulse Controls" Symmetry 16, no. 10: 1265. https://doi.org/10.3390/sym16101265
APA StyleLiu, Y., Zhuang, Y., Liu, Q., & Huang, L. (2024). Modeling and Dynamic Analysis of Algae–Fish Model with Two State-Dependent Impulse Controls. Symmetry, 16(10), 1265. https://doi.org/10.3390/sym16101265