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学者姓名：陈凤德
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Abstract ：
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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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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This paper investigates a two-species amensalism model that includes the fear effect on the first species and the Beddington-DeAngelis functional response. The existence and stability of possible equilibria are investigated. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, global dynamics analysis of the model is performed. It is observed that under certain parameter conditions, when the intensity of the fear effect is below a certain threshold value, as the fear effect increases it will only reduce the density of the first species population and will have no influence the extinction or existence of the first species population. However, when the fear effect exceeds this threshold, the increase of the fear effect will accelerate the extinction of the first species population. Finally, numerical simulations are performed to validate theoretical results.
Keyword ：
Amensalism model Amensalism model Beddington-DeAngelis functional response Beddington-DeAngelis functional response bifurcation bifurcation fear effect fear effect global dynamics global dynamics stability stability
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| GB/T 7714 | Zhu, Qun , Chen, Fengde , Li, Zhong et al. Global Dynamics of Two-Species Amensalism Model with Beddington-DeAngelis Functional Response and Fear Effect [J]. | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS , 2024 , 34 (06) . |
| MLA | Zhu, Qun et al. "Global Dynamics of Two-Species Amensalism Model with Beddington-DeAngelis Functional Response and Fear Effect" . | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 34 . 06 (2024) . |
| APA | Zhu, Qun , Chen, Fengde , Li, Zhong , Chen, Lijuan . Global Dynamics of Two-Species Amensalism Model with Beddington-DeAngelis Functional Response and Fear Effect . | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS , 2024 , 34 (06) . |
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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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We have combined cooperative hunting, inspired by recent experimental studies on birds and vertebrates, to develop a predator -prey model in which the fear effect simultaneously influences the birth and mortality rates of the prey. This differs significantly from the fear effect described by most scholars. We have made a comprehensive analysis of the dynamics of the model and obtained some new conclusions. The results indicate that both fear and cooperative hunting can be a stable or unstable force in the system. The fear can increase the density of the prey, which is different from the results of all previous scholars, and is a new discovery in our study of the fear effect. Another new finding is that fear has an opposite effect on the densities of two species, which is different from the results of most other scholars in that fear synchronously reduces the densities of both species. Numerical simulations have also revealed that the fear effect extends the time required for the population to reach its survival state and accelerates the process of population extinction.
Keyword ：
bifurcation bifurcation cooperative hunting cooperative hunting fear effect fear effect prey-predator prey-predator
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| GB/T 7714 | Xue, Yalong , Chen, Fengde , Xie, Xiangdong et al. An analysis of a predator-prey model in which fear reduces prey birth and death rates [J]. | AIMS MATHEMATICS , 2024 , 9 (5) : 12906-12927 . |
| MLA | Xue, Yalong et al. "An analysis of a predator-prey model in which fear reduces prey birth and death rates" . | AIMS MATHEMATICS 9 . 5 (2024) : 12906-12927 . |
| APA | Xue, Yalong , Chen, Fengde , Xie, Xiangdong , Chen, Shengjiang . An analysis of a predator-prey model in which fear reduces prey birth and death rates . | AIMS MATHEMATICS , 2024 , 9 (5) , 12906-12927 . |
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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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In this work, we propose and study a two species Lotka-Volterra competition model, where the first species experiences the mate-finding Allee effect caused by the second species. First, we study the presence and stability of all conceivable positive equilibria and boundary equilibria of this system. Next, by utilizing the Sotomayor theorem, we demonstrate that, given appropriate parameter circumstances, both a saddle-node bifurcation and a transcritical bifurcation exist. Finally, numerical simulations were carried out to validate our theoretical results further. We found that under certain conditions, the system appears to be bistable when the trait-mediated indirect effect is low. However, when the trait-mediated indirect effect is too high, the bistability of the system disappears, and the first species eventually tends to extinction.
Keyword ：
Bifurcation Bifurcation Competition model Competition model Mate finding Allee effect Mate finding Allee effect Stability Stability
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| GB/T 7714 | Zhu, Qun , Chen, Fengde . Impact of Fear on Searching Efficiency of First Species: A Two Species Lotka-Volterra Competition Model with Weak Allee Effect [J]. | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS , 2024 , 23 (3) . |
| MLA | Zhu, Qun et al. "Impact of Fear on Searching Efficiency of First Species: A Two Species Lotka-Volterra Competition Model with Weak Allee Effect" . | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 23 . 3 (2024) . |
| APA | Zhu, Qun , Chen, Fengde . Impact of Fear on Searching Efficiency of First Species: A Two Species Lotka-Volterra Competition Model with Weak Allee Effect . | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS , 2024 , 23 (3) . |
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In this paper, a predator-prey system with multiple anti-predator behaviors is developed and studied, where not only the prey may spread between patches but also the fear effect and counter-attack behavior of the prey are taken into account. First, the stability and existence of coexistence equilibria are presented. The unique positive equilibrium may be a saddle-node or a cusp of codimension 2. Then, various transversality conditions of bifurcations such as saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation are obtained. Moreover, compared with a single strategy, the multiple anti-predator strategies are more beneficial to the persistence and the population density of prey.
Keyword ：
Anti-Predator Anti-Predator Bifurcations Bifurcations Patch Patch Predator-Prey Predator-Prey
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| GB/T 7714 | Xia, Yue , Huang, Xinhao , Chen, Fengde et al. STABILITY AND BIFURCATION OF A PREDATOR-PREY SYSTEM WITH MULTIPLE ANTI-PREDATOR BEHAVIORS [J]. | JOURNAL OF BIOLOGICAL SYSTEMS , 2024 . |
| MLA | Xia, Yue et al. "STABILITY AND BIFURCATION OF A PREDATOR-PREY SYSTEM WITH MULTIPLE ANTI-PREDATOR BEHAVIORS" . | JOURNAL OF BIOLOGICAL SYSTEMS (2024) . |
| APA | Xia, Yue , Huang, Xinhao , Chen, Fengde , Chen, Lijuan . STABILITY AND BIFURCATION OF A PREDATOR-PREY SYSTEM WITH MULTIPLE ANTI-PREDATOR BEHAVIORS . | JOURNAL OF BIOLOGICAL SYSTEMS , 2024 . |
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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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A Lotka-Volterra predator prey system incorporating fear effect of the prey species and density dependent death rate of predator species is proposed and studied in this paper. Local and global stability property of the equilibria are investigated. Our study shows that the density dependent death rate of predator species has no influence to the persistent or extinction property of the system. However, with the increasing of the density dependent death rate, the final density of the predator species is decreasing and the final density of the prey species is increasing. Hence, the increasing of the the density dependent death rate enhance the possibility of the extinction of the predator specie. Numeric simulations show that too high density dependent death rate and too high fear effect of prey species may lead to the extinction of the predator species. Copyright © 2023 Korean Society of Gastrointestinal Endoscopy.
Keyword ：
Density dependent death rate Density dependent death rate Fear effect Fear effect Lotka-Volterra predator prey model Lotka-Volterra predator prey model Stability Stability
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| GB/T 7714 | Li, Q. , Zhu, Q. , Chen, F. . The Influence of Density Dependent Death Rate of Predator Species to the Lotka-Volterra Predator Prey System with Fear Effect [J]. | WSEAS Transactions on Systems , 2023 , 22 : 330-337 . |
| MLA | Li, Q. et al. "The Influence of Density Dependent Death Rate of Predator Species to the Lotka-Volterra Predator Prey System with Fear Effect" . | WSEAS Transactions on Systems 22 (2023) : 330-337 . |
| APA | Li, Q. , Zhu, Q. , Chen, F. . The Influence of Density Dependent Death Rate of Predator Species to the Lotka-Volterra Predator Prey System with Fear Effect . | WSEAS Transactions on Systems , 2023 , 22 , 330-337 . |
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