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学者姓名：陈凤德
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Abstract ：
This paper is the first to propose an allelopathic phytoplankton competition ODE model influenced by the fear effect based on natural biological phenomena. It is shown that the interplay of this fear effect and the allelopathic term cause rich dynamics in the proposed competition model, such as global stability, transcritical bifurcation, pitchfork bifurcation, and saddle-node bifurcation. We also consider the spatially explicit version of the model and prove analogous results. Numerical simulations verify the feasibility of the theoretical analysis. The results demonstrate that the primary cause of the extinction of non-toxic species is the fear of toxic species compared to toxins. Allelopathy only affects the density of non-toxic species. The discussion guides the conservation of species and the maintenance of biodiversity.
Keyword ：
Allelopathy Allelopathy Competition Competition Global stability Global stability Pitchfork bifurcation Pitchfork bifurcation Reaction-diffusion system Reaction-diffusion system Saddle-node bifurcation Saddle-node bifurcation Transcritical bifurcation Transcritical bifurcation
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| GB/T 7714 | Chen, Shangming , Chen, Fengde , Srivastava, Vaibhava et al. Dynamical Analysis of an Allelopathic Phytoplankton Model with Fear Effect [J]. | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS , 2024 , 23 (4) . |
| MLA | Chen, Shangming et al. "Dynamical Analysis of an Allelopathic Phytoplankton Model with Fear Effect" . | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 23 . 4 (2024) . |
| APA | Chen, Shangming , Chen, Fengde , Srivastava, Vaibhava , Parshad, Rana D. . Dynamical Analysis of an Allelopathic Phytoplankton Model with Fear Effect . | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS , 2024 , 23 (4) . |
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Amensalism, a rare yet impactful symbiotic relationship in ecological systems, is the focus of this study. We examine a discrete-time amensalism system by incorporating the fear effect on the first species. We identify the plausible equilibrium points and analyze their local stability conditions. The global attractivity of the positive equilibrium, E*, and the boundary equilibrium, E1, are analyzed by exploring threshold conditions linked to the level of fear. Additionally, we analyze transcritical bifurcations and flip bifurcations exhibited by the boundary equilibrium points analytically. Considering some biologically feasible parameter values, we conduct extensive numerical simulations. From numerical simulations, it is observed that the level of fear has a stabilizing effect on the system dynamics when it increases. It eventually accelerates the extinction process for the first species as the level of fear continues to increase. These findings highlight the complex interplay between external factors and intrinsic system dynamics, enriching potential mechanisms for driving species changes and extinction events.
Keyword ：
amensalism amensalism chaos control chaos control fear effect fear effect flip bifurcation flip bifurcation global attractivity global attractivity transcritical bifurcation transcritical bifurcation
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| GB/T 7714 | Li, Qianqian , Kashyap, Ankur Jyoti , Zhu, Qun et al. Dynamical behaviours of discrete amensalism system with fear effects on first species [J]. | MATHEMATICAL BIOSCIENCES AND ENGINEERING , 2024 , 21 (1) : 832-860 . |
| MLA | Li, Qianqian et al. "Dynamical behaviours of discrete amensalism system with fear effects on first species" . | MATHEMATICAL BIOSCIENCES AND ENGINEERING 21 . 1 (2024) : 832-860 . |
| APA | Li, Qianqian , Kashyap, Ankur Jyoti , Zhu, Qun , Chen, Fengde . Dynamical behaviours of discrete amensalism system with fear effects on first species . | MATHEMATICAL BIOSCIENCES AND ENGINEERING , 2024 , 21 (1) , 832-860 . |
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In this paper, a single-species logistic model with both fear effect-type feedback control and additive Allee effect is developed and investigated using the new coronavirus as a feedback control variable. When the system introduces additive Allee effect and fear effect-type feedback control, more complicated dynamical behavior is obtained. The system can undergo transcritical bifurcation, saddle-node bifurcation, degenerate Hopf bifurcation and Bogdanov-Takens bifurcation. By numerical simulations, the system exhibits homoclinic bifurcation and saddle-node bifurcation of limit cycles as parameters are altered. Remarkably, it is the first time that two limit cycles have been discovered in a single-species logistic model with the Allee effect. Further, stronger Allee effect or stronger fear effect can lead to the extinction of the species population.
Keyword ：
additive Allee effect additive Allee effect bifurcation bifurcation fear effect-type feedback control fear effect-type feedback control Logistic model Logistic model two limit cycles two limit cycles
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| GB/T 7714 | Zhu, Qun , Li, Zhong , Chen, Fengde . Bifurcation in a single-species logistic model with addition Allee effect and fear effect-type feedback control [J]. | INTERNATIONAL JOURNAL OF BIOMATHEMATICS , 2024 . |
| MLA | Zhu, Qun et al. "Bifurcation in a single-species logistic model with addition Allee effect and fear effect-type feedback control" . | INTERNATIONAL JOURNAL OF BIOMATHEMATICS (2024) . |
| APA | Zhu, Qun , Li, Zhong , Chen, Fengde . Bifurcation in a single-species logistic model with addition Allee effect and fear effect-type feedback control . | INTERNATIONAL JOURNAL OF BIOMATHEMATICS , 2024 . |
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We propose a class of amensalism population models in which the refuge is related to the density of the second population. For the autonomous case, we obtain precise thresholds that guarantee the extinction or stable survival of the first population. For the non-autonomous case, sufficient conditions are obtained to ensure the system’s persistence, global asymptotical stability, and extinction, respectively. We demonstrate the feasibility of the main results with the help of numerical simulations. © 2024, International Association of Engineers. All rights reserved.
Keyword ：
Ammensalism Ammensalism Global stability Global stability Local stability Local stability Refuge Refuge
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| GB/T 7714 | Chong, Y. , Zhu, Q. , Li, Q. et al. Dynamic Behaviors of a Two Species Amensalism Model with a Second Species Dependent Cover [J]. | Engineering Letters , 2024 , 32 (8) : 1553-1561 . |
| MLA | Chong, Y. et al. "Dynamic Behaviors of a Two Species Amensalism Model with a Second Species Dependent Cover" . | Engineering Letters 32 . 8 (2024) : 1553-1561 . |
| APA | Chong, Y. , Zhu, Q. , Li, Q. , Chen, F. . Dynamic Behaviors of a Two Species Amensalism Model with a Second Species Dependent Cover . | Engineering Letters , 2024 , 32 (8) , 1553-1561 . |
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By using model discretization of the piecewise constant argument method, a discrete amensalism model with nonselective harvesting and Allee effect is formulated. The dynamic analysis of the model is studied and the existence and stability of the equilibrium point are discussed. The fold bifurcation and flip bifurcation at the equilibrium point of the system are proved by using the bifurcation theory and the center manifold theorem. In order to control flip bifurcation and restore the system to a stable state, a hybrid control strategy of parameter perturbation and state feedback is adopted. Finally, the effectiveness of the theoretical results and the control strategy is verified by numerical simulations.
Keyword ：
chaos control chaos control flip bifurcation flip bifurcation fold bifurcation fold bifurcation Stability Stability
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| GB/T 7714 | Hu, Xinli , Li, Hanghang , Chen, Fengde . Bifurcation Analysis of a Discrete Amensalism Model [J]. | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS , 2024 , 34 (02) . |
| MLA | Hu, Xinli et al. "Bifurcation Analysis of a Discrete Amensalism Model" . | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 34 . 02 (2024) . |
| APA | Hu, Xinli , Li, Hanghang , Chen, Fengde . Bifurcation Analysis of a Discrete Amensalism Model . | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS , 2024 , 34 (02) . |
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The dynamic behavior of a discrete-time two-patch model with the Allee effect and nonlinear dispersal is studied in this paper. The model consists of two patches connected by the dispersal of individuals. Each patch has its own carrying capacity and intraspecific competition, and the growth rate of one patch exhibits the Allee effect. The existence and stability of the fixed points for the model are explored. Then, utilizing the central manifold theorem and bifurcation theory, fold and flip bifurcations are investigated. Finally, numerical simulations are conducted to explore how the Allee effect and nonlinear dispersal affect the dynamics of the system. © 2024 the Author(s)
Keyword ：
Bifurcation (mathematics) Bifurcation (mathematics)
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| GB/T 7714 | Gao, Minjuan , Chen, Lijuan , Chen, Fengde . Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal [J]. | Mathematical Biosciences and Engineering , 2024 , 21 (4) : 5499-5520 . |
| MLA | Gao, Minjuan et al. "Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal" . | Mathematical Biosciences and Engineering 21 . 4 (2024) : 5499-5520 . |
| APA | Gao, Minjuan , Chen, Lijuan , Chen, Fengde . Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal . | Mathematical Biosciences and Engineering , 2024 , 21 (4) , 5499-5520 . |
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China’s birth rate has declined, but its mortality rate has risen year after year due to the new coronavirus pandemic. Using the new coronavirus pandemic as a feedback control variable, we proposed a new non-autonomous single-population feedback control model in which the feedback control variable reduces the population’s birth rate while increasing the population’s mortality rate. We determined sufficient conditions for the persistence, extinction, and global stability. The analytical results are then compared numerically with relevant examples. © 2024, International Association of Engineers. All rights reserved.
Keyword ：
Adaptive control systems Adaptive control systems Coronavirus Coronavirus Feedback control Feedback control Population statistics Population statistics
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| GB/T 7714 | Yue, Qin , Jyoti, Ankur , Chen, Fengde . Dynamic Behaviors of a Non-autonomous Single-Species Feedback Control System [J]. | Engineering Letters , 2024 , 32 (7) : 1291-1299 . |
| MLA | Yue, Qin et al. "Dynamic Behaviors of a Non-autonomous Single-Species Feedback Control System" . | Engineering Letters 32 . 7 (2024) : 1291-1299 . |
| APA | Yue, Qin , Jyoti, Ankur , Chen, Fengde . Dynamic Behaviors of a Non-autonomous Single-Species Feedback Control System . | Engineering Letters , 2024 , 32 (7) , 1291-1299 . |
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The commensal symbiosis system with the Allee effect and single feedback control is proposed and analyzed in this paper. The stability analysis of all possible equilibrium points is discussed, and the sufficient conditions for global stability of the interior equilibrium points are obtained. The occurrence of transcritical bifurcation and saddle-node bifurcation around the equilibrium points is investigated. Finally, the main results of the model are illustrated by numerical simulations. © (2024), (International Association of Engineers). All rights reserved.
Keyword ：
Allee effect Allee effect commensalism model commensalism model saddle-node bifurcation saddle-node bifurcation single feedback control single feedback control transcritical bifurcation transcritical bifurcation
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| GB/T 7714 | Xu, L. , Xue, Y. , Lin, Q. et al. Stability and Bifurcation Analysis of Commensal Symbiosis System with the Allee Effect and Single Feedback Control [J]. | IAENG International Journal of Applied Mathematics , 2024 , 54 (8) : 1586-1596 . |
| MLA | Xu, L. et al. "Stability and Bifurcation Analysis of Commensal Symbiosis System with the Allee Effect and Single Feedback Control" . | IAENG International Journal of Applied Mathematics 54 . 8 (2024) : 1586-1596 . |
| APA | Xu, L. , Xue, Y. , Lin, Q. , Chen, F. . Stability and Bifurcation Analysis of Commensal Symbiosis System with the Allee Effect and Single Feedback Control . | IAENG International Journal of Applied Mathematics , 2024 , 54 (8) , 1586-1596 . |
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This paper presents a study on a Lotka-Volterra ammensalism model that incorporates the fear effect, which can potentially decrease the birth rate and raise the mortality rate of the species. For the autonomous case, equilibrium points’ local and global stability are discussed. For the nonautonomous case, sufficient conditions which ensure the persistence and extinction, and global asymptotic stability of the positive so-lutions are obtained, respectively. The study has shown that with the increase of the fear effect, the final density of the affected population will decrease, and when the fear effect is large enough, it will cause population’s extinction. © 2024, International Association of Engineers. All rights reserved.
Keyword ：
Ammensalism Ammensalism Extinction Extinction Fear effect Fear effect Global asymptotically stability Global asymptotically stability Global stability Global stability Local stability Local stability Persistence Persistence
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| GB/T 7714 | Chong, Y. , Hou, Y. , Chen, S. et al. The Influence of Fear Effect to the Dynamic Behaviors of Lotka-Volterra Ammensalism Model [J]. | Engineering Letters , 2024 , 32 (6) : 1233-1242 . |
| MLA | Chong, Y. et al. "The Influence of Fear Effect to the Dynamic Behaviors of Lotka-Volterra Ammensalism Model" . | Engineering Letters 32 . 6 (2024) : 1233-1242 . |
| APA | Chong, Y. , Hou, Y. , Chen, S. , Chen, F. . The Influence of Fear Effect to the Dynamic Behaviors of Lotka-Volterra Ammensalism Model . | Engineering Letters , 2024 , 32 (6) , 1233-1242 . |
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In this paper, a two-patch model with additive Allee effect, nonlinear dispersal and commensalism is proposed and studied. The stability of equilibria and the existence of saddle-node bifurcation, transcritical bifurcation are discussed. Through qualitative analysis of the model, we know that the persistence and the extinction of population are influenced by the Allee effect, dispersal and commensalism. Combining with numerical simulation, the study shows that the total population density will increase when the Allee effect constant a increases or m decreases. In addition to suppress the Allee effect, nonlinear dispersal and commensalism are crucial to the survival of the species in the two patches.
Keyword ：
additive Allee effect additive Allee effect bifurcation bifurcation Commensalism Commensalism nonlinear dispersal nonlinear dispersal stability stability
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| GB/T 7714 | Zhong, Jin , Chen, Lijuan , Chen, Fengde . Stability and bifurcation in a two-patch commensal symbiosis model with nonlinear dispersal and additive Allee effect [J]. | INTERNATIONAL JOURNAL OF BIOMATHEMATICS , 2024 . |
| MLA | Zhong, Jin et al. "Stability and bifurcation in a two-patch commensal symbiosis model with nonlinear dispersal and additive Allee effect" . | INTERNATIONAL JOURNAL OF BIOMATHEMATICS (2024) . |
| APA | Zhong, Jin , Chen, Lijuan , Chen, Fengde . Stability and bifurcation in a two-patch commensal symbiosis model with nonlinear dispersal and additive Allee effect . | INTERNATIONAL JOURNAL OF BIOMATHEMATICS , 2024 . |
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