A Complete Classification on the Center-Focus Problem of a Generalized Cubic Kukles System with a Nilpotent Singular Point

Li, Feng; Chen, Ting; Liu, Yuanyuan; Yu, Pei

doi:10.1007/s12346-023-00863-3

Qual. Theory Dyn. Syst.

2023

DOI: 10.1007/s12346-023-00863-3

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A Complete Classification on the Center-Focus Problem of a Generalized Cubic Kukles System with a Nilpotent Singular Point

Feng Li,

Ting Chen,

Yuanyuan Liu

et al.

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2024

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Cited by 2 publications

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Nilpotent global centers of generalized polynomial Kukles system with degree three

Chen,

Feng,

Zhang

2024

Proc. Amer. Math. Soc.

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Nilpotent global centers of generalized polynomial Kukles system with degree three

Chen,

Feng,

Zhang

2024

Proc. Amer. Math. Soc.

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Global dynamics of a diffusive competitive Lotka–Volterra model with advection term and more general nonlinear boundary condition

Zhou,

2024

Adv Cont Discr Mod

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We investigate a competitive diffusion–advection Lotka–Volterra model with more general nonlinear boundary condition. Based on some new ideas, techniques, and the theory of the principal spectral and monotone dynamical systems, we establish the influence of the following parameters on the dynamical behavior of system (1.2): advection rates $\alpha _{u}$ α u and $\alpha _{v}$ α v , interspecific competition intensities $c_{u}$ c u and $c_{v}$ c v , the resources functions $r_{u}$ r u and $r_{v}$ r v of the two competitive species, and nonlinear boundary functions $g_{1}$ g 1 and $g_{2}$ g 2 . The models of (Tang and Chen in J. Differ. Equ. 269(2):1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264:4176–4198, 2018) are particular cases of our results when $g_{i}\equiv const$ g i ≡ c o n s t for $i=1,2$ i = 1 , 2 , and hence this paper extends some of the conclusions from (Tang and Chen in J. Differ. Equ. 269(2):1465–1483, 2020; Zhou and Zhao in J. Differ. Equ. 264:4176–4198, 2018).

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A Complete Classification on the Center-Focus Problem of a Generalized Cubic Kukles System with a Nilpotent Singular Point

Cited by 2 publications

References 25 publications

Nilpotent global centers of generalized polynomial Kukles system with degree three

Nilpotent global centers of generalized polynomial Kukles system with degree three

Global dynamics of a diffusive competitive Lotka–Volterra model with advection term and more general nonlinear boundary condition

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