Dynamic behaviors of a stage structure amensalism system with a cover for the first species

Lei, Chaoquan

doi:10.1186/s13662-018-1729-1

Cited by 17 publications

(5 citation statements)

References 22 publications

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“…Since then, many scholars have conducted extensive research on the amensalism model based on the model (1). For example, nonlinear functional response [3,13,14], Allee effect [15][16][17][18][19], and a cover (i.e., refuge) [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species

Zhou¹,

Chen²,

Lin³

2022

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Of interest is the dynamics of the discrete-time amensalism model with a cover on the first species. We first obtain the existence and stability of fixed points and the conditions for the permanent coexistence of two species. Then we demonstrate the occurrence of flip bifurcation by using the central manifold theorem and bifurcation theory. A hybrid control strategy is used to control the flip bifurcation and stabilize unstable periodic orbits embedded in the complex attractor. Numerical simulation verifies the feasibility of theoretical analysis and reveals some novel and exciting dynamic phenomena.

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Section: Introductionmentioning

confidence: 99%

Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species

Zhou¹,

Chen²,

Lin³

2022

Axioms

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“…During the last decade, many scholars have studied the stage structure model of species (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and references therein), and many interesting characteristic features of the stage structure model were obtained.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis in a single-species stage structure system with Michaelis–Menten-type harvesting

Zhu

Lai

et al. 2020

Adv Differ Equ

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In this paper, we prpose a single-species stage structure model with Michaelis–Menten-type harvesting for mature population. We investigate the existence of all possible equilibria of the system and discuss the stability of equilibria. We use Sotomayor’s theorem to derive the conditions for the existence of saddle-node and transcritical bifurcations. From the ecological point of view, we analyze the effect of harvesting on the model of mature population and consider it as a bifurcation parameter, giving the maximum threshold of continuous harvesting. By constructing a Lyapunov function and Bendixson–Dulac discriminant, we give sufficient conditions for the global stability of boundary equilibrium and positive equilibrium, respectively. Our study shows that nonlinear harvesting may lead to a complex dynamic behavior of the system, which is quite different from linear harvesting. We carry out numeric simulations to verify the feasibility of the main results.

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“…On the other hand, many scholars investigated the dynamic behaviors of the stagestructured species, see [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], and the references cited therein. In constructing a stagestructured model, two different ideas were applied.…”

Section: Introductionmentioning

confidence: 99%

“…They finally drew the conclusion: the cooperation between the species has no influence on the persistence property of the system. Another way to construct a stage-structured ecosystem is to assume that there is a proportional number of immature species that become mature species [40,41,43,44]. Recently, Khajanchi and Banerjee [41] proposed the following stage-structured predatorprey model with ratio-dependent functional response:…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of a stage-structured commensalism system

Lei

2018

Adv Differ Equ

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A two species stage-structured commensalism model is proposed and studied in this paper. Local and global stability property of the boundary equilibrium and the positive equilibrium are investigated, respectively. If the stage-structured species is extinct, then depending on the intensity of cooperation, the species may still be extinct or become persistent. If the stage-structured species is permanent, then the final system is always globally asymptotically stable, which means the species is always permanent. Our study shows that increasing the intensity of the cooperation between the species is one of very useful methods to avoid extinction of the endangered species. Such a finding may be useful in protecting the endangered species. An example together with its numeric simulations is presented to verify our main results. MSC: 34C25; 92D25; 34D20; 34D40

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Dynamic behaviors of a stage structure amensalism system with a cover for the first species

Cited by 17 publications

References 22 publications

Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species

Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species

Stability and bifurcation analysis in a single-species stage structure system with Michaelis–Menten-type harvesting

Dynamic behaviors of a stage-structured commensalism system

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