Dynamic analysis of phytoplankton–zooplankton–fish singular perturbation system on three time-scales
In this paper, a three-time scale plankton–fish singular perturbation system is proposed by considering the Beddington–DeAngelis functional response and intraguild predation (IGP). For (1, 2)-fast–slow systems, the singularity and classification of generic fold points are discussed. The small amplit...
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| Veröffentlicht in: | Chaos, solitons and fractals Jg. 190; S. 115711 |
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| Sprache: | Englisch |
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| ISSN: | 0960-0779 |
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| Abstract | In this paper, a three-time scale plankton–fish singular perturbation system is proposed by considering the Beddington–DeAngelis functional response and intraguild predation (IGP). For (1, 2)-fast–slow systems, the singularity and classification of generic fold points are discussed. The small amplitude oscillations (SAOs) will generate around the weak characteristic direction near the folded node, which provides a theoretical reference for effectively predicting the phenomenon of algal blooms. It is also obtained that the small amplitude oscillation cannot be generated by the singular Hopf bifurcation and the folded node mechanism. For (2, 1)-fast–slow systems, the existence of singular Hopf bifurcation is discussed by using the center manifold reduction method. The stability of the periodic solution of the singular Hopf bifurcation is discussed. Furthermore, the existence and uniqueness of the relaxation oscillation in R3 are researched by using the entry–exit function. In addition, the effect of stochastic factors on the singular perturbation system is considered.
•The small amplitude oscillations generate near the folded node.•Small amplitude oscillation is the precursor of algal blooms.•The singular Hopf bifurcation in R3 is proved by using the center manifold reduction.•The stable singular Hopf bifurcation is the premise of the optimal fishing point.•The relaxation oscillation in R3 is researched by using the entry–exit function. |
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| AbstractList | In this paper, a three-time scale plankton–fish singular perturbation system is proposed by considering the Beddington–DeAngelis functional response and intraguild predation (IGP). For (1, 2)-fast–slow systems, the singularity and classification of generic fold points are discussed. The small amplitude oscillations (SAOs) will generate around the weak characteristic direction near the folded node, which provides a theoretical reference for effectively predicting the phenomenon of algal blooms. It is also obtained that the small amplitude oscillation cannot be generated by the singular Hopf bifurcation and the folded node mechanism. For (2, 1)-fast–slow systems, the existence of singular Hopf bifurcation is discussed by using the center manifold reduction method. The stability of the periodic solution of the singular Hopf bifurcation is discussed. Furthermore, the existence and uniqueness of the relaxation oscillation in R3 are researched by using the entry–exit function. In addition, the effect of stochastic factors on the singular perturbation system is considered.
•The small amplitude oscillations generate near the folded node.•Small amplitude oscillation is the precursor of algal blooms.•The singular Hopf bifurcation in R3 is proved by using the center manifold reduction.•The stable singular Hopf bifurcation is the premise of the optimal fishing point.•The relaxation oscillation in R3 is researched by using the entry–exit function. |
| ArticleNumber | 115711 |
| Author | Zhang, Yue Ai, Xin |
| Author_xml | – sequence: 1 givenname: Xin surname: Ai fullname: Ai, Xin – sequence: 2 givenname: Yue surname: Zhang fullname: Zhang, Yue email: zhangyue@mail.neu.edu.cn |
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| Keywords | Relaxation oscillation Small amplitude oscillation Center manifold reduction Stochastic singular perturbation system Singular Hopf bifurcation |
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| SubjectTerms | Center manifold reduction Relaxation oscillation Singular Hopf bifurcation Small amplitude oscillation Stochastic singular perturbation system |
| Title | Dynamic analysis of phytoplankton–zooplankton–fish singular perturbation system on three time-scales |
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