DYNAMICS OF A TWO-PREY AND ONE PREDATOR SYSTEM WITH QUADRATIC SELF INTERACTION

Lingling Liu; Ke-wei Ding; Zhiheng Yu

doi:10.11948/20220524

2023 Volume 13 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(5): 2670-2681

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Lingling Liu, Ke-wei Ding, Zhiheng Yu. DYNAMICS OF A TWO-PREY AND ONE PREDATOR SYSTEM WITH QUADRATIC SELF INTERACTION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2670-2681. doi: 10.11948/20220524

Citation:

Lingling Liu, Ke-wei Ding, Zhiheng Yu. DYNAMICS OF A TWO-PREY AND ONE PREDATOR SYSTEM WITH QUADRATIC SELF INTERACTION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2670-2681. doi: 10.11948/20220524

DYNAMICS OF A TWO-PREY AND ONE PREDATOR SYSTEM WITH QUADRATIC SELF INTERACTION

1.
School of Sciences and Institute for Artificial Intelligence, Southwest Petroleum University, 610500 Chengdu, China
2.
School of Computer Science and Technology, Southwest Minzu University, 610041 Chengdu, China
3.
School of Mathematics, Southwest Jiaotong University, 610031 Chengdu, China

Author Bio: Email: a600aa@163.com(L. Liu); Email: bluedkw@163.com(K. Ding)
Corresponding author: Email: yuzhiheng9@163.com(Z. Yu)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 12171337), China Scholarship Council (Nos. 202108515063, 202100850001), Fundamental Research Funds for the Central Universities (No. 2021128) and National Science Foundation of Sichuan Province (Nos. 2022NSFSC1834, 2022NSFSC1793, 2023NSFSC0064)

Abstract

Abstract

A two-prey and one-predator system with quadratic self-interaction is discussed on subsets of special biological sense, none of which is closed under operations of the polynomial ring. The known work studied the stability of the boundary equilibria and gave invariant algebraic surfaces up to degree two but no further discussion for bifurcations. In this paper, we investigate the finite and infinite equilibria and their qualitative properties in the first octant. Moreover, we discuss their bifurcations, such as transcritical bifurcation on boundary equilibria, and give the bifurcation diagram. Finally, simulation examples are given to illustrate the theoretical results in this paper.
- Coexistence /
- stability /
- saddle-node /
- transcritical bifurcation
MSC: 34C23, 34C60, 37G10

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References

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