Bifurcation analysis of a new aquatic ecological model with aggregation effect

Li, Xinxin; Yu, Hengguo; Dai, Chuanjun; Ma, Zengling; Wang, Qi; Zhao, Min

doi:10.1016/j.matcom.2021.05.015

Cited by 13 publications

(5 citation statements)

References 37 publications

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“…Based on the above analysis, we can see that the filter-feeding fish have been thought to be suited to control algal blooms directly in the subtropical lake reservoir, some similar research results can be seen in the paper [22] [23] [24] [25].…”

Section: Introductionmentioning

confidence: 62%

Population Interaction Dynamics Analysis of an Algae-Fish System

Zhuang¹,

Yan²,

Xie³

et al. 2022

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Section: Introductionmentioning

confidence: 62%

Population Interaction Dynamics Analysis of an Algae-Fish System

Zhuang¹,

Yan²,

Xie³

et al. 2022

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“…In the follow-up research works, we will first deepen theoretical research of bifurcation dynamics by learning from relevant results in these papers [39][40][41], and then further explore the dynamic behavior of patch pattern in ecosystem in the help of these papers [42][43][44], finally put mathematical models in specific ecological and environmental problems to study their ecological significance by means of these papers [45][46][47]. In a word, all these results are expected to be useful in studying dynamic behavior of the ecosystem.…”

Section: Discussionmentioning

confidence: 99%

Equilibria and Bogdanov‐Takens Bifurcation Analysis in the Bazykin’s Predator‐Prey System

Wang

2022

Discrete Dynamics in Nature and Society

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In the paper, we proposed a Bazykin’s predator-prey system to explore the equilibrium point and Bogdanov-Takens bifurcation problems. Firstly, we derived some key parameter threshold conditions to ensure that the Bazykin’s predator-prey system had a multiple focus of multiplicity one, weak focus of order 2, cusps of codimension 2 and a degenerate Bogdanov-Takens singularity (focus or center case) of codimension 3. Furthermore, the distinction of two types of codimension 2 cusps was also discussed, which showed that the threshold of the two types of cusps could exhibit a cusp, which was a special case of the mentioned degenerate Bogdanov-Takens singularity (focus or center case) of codimension 3. Secondly, we systematically calculated that the Bazykin’s predator-prey system could undergo two types of Bogdanov-Takens bifurcations of codimension 2 and a degenerate focus type Bogdanov-Takens bifurcation of codimension 3. Finally, some numerical examples were implemented to verify the correctness and feasibility of mathematical theory derivation, which also directly showed all possible equilibrium points and Bogdanov-Takens bifurcations of Bazykin’s predator-prey system. In a word, all the research results could play an important theoretical support role in the study of controlling cyanobacteria bloom.

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“…At present, it is of special significance to apply ecological models to study the problem of biological algae control, this is because that ecological model can form three basic of studying biological system, namely: trophic level analysis, system perspective and dynamic view [21] [22], which can improve the understanding of the ecological interactions between populations and their dependence on internal and external conditions [23] [24]. The paper [12] proposed a new aquatic ecological model to explore the aggregation behavior of algae population. According to the modeling framework of this new aquatic ecological model, we will propose an aquatic ecological model to characterize the dynamic relationship between algae and protozoa (protozoa can feed on algae), which can be described as follow:…”

Section: Ecological Mathematical Modelingmentioning

confidence: 99%

“…The paper [11] pointed out that silver and bighead carps were just suitable for controlling cyanobacteria bloom by comparison with the increasing of blue-green algae's proportion and the forming of microcystis bloom within the enclosures without fish. The paper [12] constructed a new aquatic ecological model to understand the dynamic relationship between Microcystis aeruginosa and filter-feeding fish, which could indirectly show the algae control effect of filter-feeding fish. The paper [13] proposed an aquatic amensalism model to explore the inhibition mechanism of algicidal bacteria on algae.…”

Section: Introductionmentioning

confidence: 99%

Dynamics Analysis of an Aquatic Ecological Model with Allee Effect

Zheng¹,

Yan²,

Yu³

2022

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In this paper, based on the dynamic relationship between algae and protozoa, an aquatic ecological model with Allee effect was established to investigate how some ecological environment factors affect coexistence mode of algae and protozoa. Mathematical derivation works mainly gave some key conditions to ensure the existence and stability of all possible equilibrium points, and to induce the occurrence of transcritical bifurcation and Hopf bifurcation. The numerical simulation works mainly revealed ecological relationship change characteristics of algae and protozoa with the help of bifurcation dynamics evolution process. Furthermore, it was also worth emphasizing that Allee effect had a strong influence on the dynamic relationship between algae and protozoa. In a word, it was hoped that the research results could provide some theoretical support for algal bloom control, and also be conducive to the rapid development of aquatic ecological models.

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Bifurcation analysis of a new aquatic ecological model with aggregation effect

Cited by 13 publications

References 37 publications

Population Interaction Dynamics Analysis of an Algae-Fish System

Population Interaction Dynamics Analysis of an Algae-Fish System

Equilibria and Bogdanov‐Takens Bifurcation Analysis in the Bazykin’s Predator‐Prey System

Dynamics Analysis of an Aquatic Ecological Model with Allee Effect

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