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学者姓名：陈凤德
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Abstract ：
Fear effects, as non-consumptive interactions in ecological systems, have emerged as a critical factor influencing species coexistence and population dynamics. Understanding the impact of fear effects on competing ecosystems helps humans better protect species and maintain ecological balance. In this paper, we propose and study a special Lotka-Volterra competition system, where one competitor experiences a reduction in birth rates and an increase in mortality rates due to fear of its competitor, and the effect of fear has saturated cost parameters beta and eta. The results show that using beta and eta as bifurcation parameters can induce transcritical and saddle-node bifurcations in the system. Furthermore, we find that the introduced saturated fear cost parameters beta and eta have interesting effects on the dynamical behavior of the Lotka-Volterra system. When the saturated fear cost parameters beta and eta satisfy certain conditions, the fear parameter k does not affect the global stability of equilibria. Even under extreme fear, the two species are still able to coexist stably, which aligns with certain ecological phenomena. All theoretical results are verified through numerical simulations.
Keyword ：
bifurcation bifurcation Competition model Competition model saturated fear effects saturated fear effects stability stability
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| GB/T 7714 | He, Guangwen , Chen, Fengde , Li, Zhong et al. The influence of saturated fear effects on species dynamics: A Lotka-Volterra competition model analysis [J]. | INTERNATIONAL JOURNAL OF BIOMATHEMATICS , 2025 . |
| MLA | He, Guangwen et al. "The influence of saturated fear effects on species dynamics: A Lotka-Volterra competition model analysis" . | INTERNATIONAL JOURNAL OF BIOMATHEMATICS (2025) . |
| APA | He, Guangwen , Chen, Fengde , Li, Zhong , Chen, Lijuan . The influence of saturated fear effects on species dynamics: A Lotka-Volterra competition model analysis . | INTERNATIONAL JOURNAL OF BIOMATHEMATICS , 2025 . |
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Predator-prey interactions are among the most common and crucial ecological phenomena in nature. Over the course of long-term evolution, prey populations have developed various anti-predation strategies to cope with the threat of predators, with population dispersal being one of the most common strategies. In traditional ecological models, the prey population is typically constrained by direct predation. However, an increasing body of empirical evidence suggests that the fear effect from the predator significantly alters the physiological behavior of prey, leading to a decrease in reproduction rate and an increase in mortality rate. In this paper, we investigate a predator-prey system incorporating asymmetric dispersal and the fear effect, which influences the birth and death rates of the prey species. We rigorously establish the existence and local stability of equilibrium points, derive sufficient conditions for global stability, and prove the occurrence of a transcritical bifurcation at the boundary equilibrium. Our analysis reveals an optimal dispersal rate that maximizes prey population density; beyond this threshold, increased dispersal drives both populations to extinction. Furthermore, the fear effect and its maximum cost exhibit significant negative impacts on predator abundance, though they do not alter the equilibrium stability or existence. These findings provide critical insights for designing habitat corridors in endangered species conservation and underscore the pivotal role of prey dispersal in shaping population dynamics.
Keyword ：
bifurcation bifurcation dispersal dispersal fear effect fear effect global stability global stability predator-prey predator-prey
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| GB/T 7714 | Meng, Xinyu , Chen, Lijuan , Chen, Fengde . Dynamics of a Predator-Prey System with Asymmetric Dispersal and Fear Effect [J]. | SYMMETRY-BASEL , 2025 , 17 (3) . |
| MLA | Meng, Xinyu et al. "Dynamics of a Predator-Prey System with Asymmetric Dispersal and Fear Effect" . | SYMMETRY-BASEL 17 . 3 (2025) . |
| APA | Meng, Xinyu , Chen, Lijuan , Chen, Fengde . Dynamics of a Predator-Prey System with Asymmetric Dispersal and Fear Effect . | SYMMETRY-BASEL , 2025 , 17 (3) . |
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Understanding how the fear affects biological populations will help us develop more effective ecological conservation measures. In this paper, we consider a stage-structured competition model in which one competitor fears the other, leading to an impact on reducing the birth rate of the former. First, we prove the non-negativity and boundedness of the solutions of this system and also analyze the existence and stability of the equilibria of the system. Our study shows that the fear effect greatly enriches the dynamical behavior of the originally stage-structured system. The fear parameter k makes it possible for the system to have two positive equilibria and induces transcritical bifurcation, pitchfork bifurcation, and saddle-node bifurcation. Interestingly, we find that the stage-structured competition system is more sensitive to the fear effect. Under the same conditions, a smaller value of k in system with stage structure can lead to alterations in the system's dynamic behaviors. Finally, numerical simulations are conducted to support and illustrate the theoretical results.
Keyword ：
Bifurcation Bifurcation Competition model Competition model Fear effect Fear effect Stability Stability Stage-structured Stage-structured
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| GB/T 7714 | He, Guangwen , Chen, Fengde , Li, Zhong et al. Impact of Fear on a Stage-Structured Lotka-Volterra Competition Model [J]. | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS , 2025 , 24 (4) . |
| MLA | He, Guangwen et al. "Impact of Fear on a Stage-Structured Lotka-Volterra Competition Model" . | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 24 . 4 (2025) . |
| APA | He, Guangwen , Chen, Fengde , Li, Zhong , Chen, Lijuan . Impact of Fear on a Stage-Structured Lotka-Volterra Competition Model . | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS , 2025 , 24 (4) . |
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This paper investigates a model of amensalism, in which the first species is influenced by the combined effects of refuge and fear, while the second species exhibits an additive Allee effect. The paper analyzes the existence and stability of the equilibria of the system and derives the conditions for various bifurcations. In the global structure analysis, the stability at infinity is examined, and the phenomena of global stability and bistability in the system are analyzed. Additionally, a sensitivity analysis is employed to evaluate the impact of system parameters on populations. The study reveals that refuge has a significant positive effect on the first population, and refuge's effect becomes more pronounced as the fear level increases. Under the strong Allee effect, when the initial density of the second species is low, the second species may eventually become extinct; when the initial density is high, if the refuge parameter is below a certain threshold, increasing the refuge parameter slows down the extinction of the first species, whereas, when the refuge parameter exceeds this threshold, the two species can coexist. Under the weak Allee effect, when the refuge parameter surpasses a certain threshold, the two species can achieve long-term, stable coexistence, and the threshold for the weak Allee effect is higher than that for the strong Allee effect.
Keyword ：
additive Allee effect additive Allee effect amensalism model amensalism model bifurcation bifurcation fear effect fear effect global dynamics global dynamics refuge refuge
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| GB/T 7714 | Huang, Yuting , Chen, Fengde , Chen, Lijuan et al. Dynamic Analysis of an Amensalism Model Driven by Multiple Factors: The Interwoven Impacts of Refuge, the Fear Effect, and the Allee Effect [J]. | AXIOMS , 2025 , 14 (8) . |
| MLA | Huang, Yuting et al. "Dynamic Analysis of an Amensalism Model Driven by Multiple Factors: The Interwoven Impacts of Refuge, the Fear Effect, and the Allee Effect" . | AXIOMS 14 . 8 (2025) . |
| APA | Huang, Yuting , Chen, Fengde , Chen, Lijuan , Li, Zhong . Dynamic Analysis of an Amensalism Model Driven by Multiple Factors: The Interwoven Impacts of Refuge, the Fear Effect, and the Allee Effect . | AXIOMS , 2025 , 14 (8) . |
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In this paper, a Leslie-Gower predator-prey model with simplified Holling type IV functional response and Allee effect on predator is studied. We discuss the existence and stability of equilibria, and show that the system has at most three positive equilibria. Under sufficient conditions, the system can have a weak focus of order 3, a cusp of codimension 3, a nilpotent focus or an elliptic equilibrium of codimension 3, or a nilpotent elliptic equilibrium of codimension at least 4. Also, we prove that the degenerate Hopf bifurcation of codimension 3 occurs at the anti-saddle, cusp type degenerate Bogdanov-Takens bifurcation of codimension 3 occurs at the double equilibrium, and focus or elliptic type degenerate Bogdanov-Takens bifurcation of codimension 3 occurs at the triple equilibrium. Finally, some numerical simulations show that the system can exhibit two limit cycles, a semi-stable limit cycle or a limit cycle containing a homoclinic loop. Our results imply that the predator and prey can arrive a stable state of coexistence if Allee effect is small, or the predator will be extinct if Allee effect is large.
Keyword ：
Allee effect Allee effect Bogdanov-Takens bifurcation Bogdanov-Takens bifurcation Hopf bifurcation Hopf bifurcation Simplified Holling type IV Simplified Holling type IV
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| GB/T 7714 | Zhang, Mengxin , Li, Zhong , Chen, Fengde et al. Bifurcation Analysis of a Leslie-Gower Predator-Prey Model with Allee Effect on Predator and Simplified Holling Type IV Functional Response [J]. | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS , 2025 , 24 (3) . |
| MLA | Zhang, Mengxin et al. "Bifurcation Analysis of a Leslie-Gower Predator-Prey Model with Allee Effect on Predator and Simplified Holling Type IV Functional Response" . | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 24 . 3 (2025) . |
| APA | Zhang, Mengxin , Li, Zhong , Chen, Fengde , Chen, Lijuan . Bifurcation Analysis of a Leslie-Gower Predator-Prey Model with Allee Effect on Predator and Simplified Holling Type IV Functional Response . | QUALITATIVE THEORY OF DYNAMICAL SYSTEMS , 2025 , 24 (3) . |
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This paper proposes a discrete amensalism with the BeddingtonDeAngelis functional response response and fear effect on the first species. By comparison and study of different bifurcations, the introduction of the Beddington-DeAngelis functional response not only increased the dynamical behaviour of the system, including the emergence of pitchfork bifurcation and fold bifurcation, but also reduced the rate of extinction of the first species. Furthermore, we analyze the influence of the fear effect on the system, specifically focusing on the boundary equilibrium E2 and the positive equilibrium E1 & lowast;. Our findings reveal that when the second species is in a chaotic state, due to the persistence of the second species, the fear effect may have increased the stability of the first species or accelerated the extinction of the first species; when the second species is stable, the fear effect plays an essential part in maintaining the stability of the first species. Moreover, an appropriate fear effect promotes the coexistence of the first and second species. However, if the fear effect becomes excessively large, it directly results in the extinction of the first species. The discovery further enhances the understanding of the influence generated by amensalism through the fear effect.
Keyword ：
Beddington-DeAngelis functional response Beddington-DeAngelis functional response bifurcation bifurcation Chaos control. Chaos control. fear ef- fear ef- fect fect Keywords Amensalism Keywords Amensalism
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| GB/T 7714 | Li, Qianqian , Chen, Fengde , Chen, Lijuan et al. DYNAMICAL ANALYSIS OF A DISCRETE AMENSALISM SYSTEM WITH THE BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE AND FEAR EFFECT [J]. | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION , 2025 , 15 (4) : 2089-2123 . |
| MLA | Li, Qianqian et al. "DYNAMICAL ANALYSIS OF A DISCRETE AMENSALISM SYSTEM WITH THE BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE AND FEAR EFFECT" . | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION 15 . 4 (2025) : 2089-2123 . |
| APA | Li, Qianqian , Chen, Fengde , Chen, Lijuan , Li, Zhong . DYNAMICAL ANALYSIS OF A DISCRETE AMENSALISM SYSTEM WITH THE BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE AND FEAR EFFECT . | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION , 2025 , 15 (4) , 2089-2123 . |
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This study proposes a Lotka-Volterra competition model incorporating a novel fear-based feedback control mechanism. Through theoretical analysis and numerical simulations, several important conclusions are obtained. The system admits at most two positive equilibria; while the feedback control parameter does not affect their existence, it plays a crucial role in determining their stability. A sufficiently large control intensity can enhance the stability of the positive equilibrium, thereby promoting species coexistence. The system exhibits rich bifurcation phenomena, including transcritical, pitchfork, saddle-node, Hopf, and Bogdanov-Takens bifurcations. Notably, a stable limit cycle may arise through a Hopf bifurcation. Under weak competition, the system admits at most one positive equilibrium, which is always stable regardless of the intensity of fear effects. In contrast, under strong competition, the system displays more complex dynamics, including the possible occurrence of multiple positive equilibria and intricate bifurcation structures. These results highlight the crucial role of fear-based feedback control in facilitating stable coexistence in competitive ecological systems.
Keyword ：
Bifurcation Bifurcation Competition model Competition model Fear effects Fear effects Feedback control Feedback control Limit cycle Limit cycle Stability Stability
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| GB/T 7714 | He, Guangwen , Chen, Fengde , Li, Zhong et al. Dynamical regulation of lotka-volterra competition systems: a novel fear-effect-based feedback control mechanism [J]. | NONLINEAR DYNAMICS , 2025 . |
| MLA | He, Guangwen et al. "Dynamical regulation of lotka-volterra competition systems: a novel fear-effect-based feedback control mechanism" . | NONLINEAR DYNAMICS (2025) . |
| APA | He, Guangwen , Chen, Fengde , Li, Zhong , Chen, Lijuan . Dynamical regulation of lotka-volterra competition systems: a novel fear-effect-based feedback control mechanism . | NONLINEAR DYNAMICS , 2025 . |
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This study investigates the evolutionary mechanisms and equilibrium character-istics of the China-US trade dispute through an improved ecological competition model. By quantifying tariff policies as competition intensity regulators and introducing trade elasticity parameters, we construct a dynamic system that captures the nonlinear feedback between economic rivals. Key findings are as follows. (1) When both nations implement reciprocal tariff measures with similar economic sensitivities, the system converges to a stable equilibrium where bilateral economic outputs stabilize at reduced levels compared to pre-conflict states, provided the product of adjusted competition coefficients remains below critical thresholds. (2) Excessive tariff escalation beyond identifiable tipping points triggers winner-takes-all outcomes, validating the "Thucydides Trap" hypothesis in eco-nomic conflicts. (3) Empirical simulations using 2018-2023 trade data demonstrate that China's tit-for-tat tariff strategy effectively maintains competitive balance, while domestic market expansion measures (evidenced by a 6.3% average annual growth in China's do-mestic consumption) significantly mitigate trade diversion effects. The study establishes theoretical connections with optimal tariff theory and strategic trade policy literature while providing policymakers with quantitative tools to assess trade policy impacts. Our find-ings theoretically validate China's policy combination of calibrated reciprocity and domestic demand stimulation, offering new insights into managing great-power economic competition.
Keyword ：
China's symmetric tariffs China's symmetric tariffs domestic demand domestic demand Lotka-Volterra competition model Lotka-Volterra competition model Sino-US trade dispute Sino-US trade dispute
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| GB/T 7714 | Chen, Baoguo , Chen, Fengde . Dynamic Competition Model Perspective on the China-US Trade Dispute: Why Did China Adopt Symmetric Tariffs? [J]. | MATHEMATICS , 2025 , 13 (11) . |
| MLA | Chen, Baoguo et al. "Dynamic Competition Model Perspective on the China-US Trade Dispute: Why Did China Adopt Symmetric Tariffs?" . | MATHEMATICS 13 . 11 (2025) . |
| APA | Chen, Baoguo , Chen, Fengde . Dynamic Competition Model Perspective on the China-US Trade Dispute: Why Did China Adopt Symmetric Tariffs? . | MATHEMATICS , 2025 , 13 (11) . |
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This study investigates a modified Lotka-Volterra commensalism system that incorporates the weak Allee effect in prey and symmetric (equal harvesting effort for both species) non-selective harvesting, addressing a critical gap in ecological modeling. Unlike previous work, we rigorously examine how the interaction between the Allee effect and harvesting disrupts system stability, giving rise to novel bifurcation phenomena and population collapse thresholds. Using eigenvalue analysis and the Dulac-Bendixson criterion, we derive sufficient conditions for the existence and stability of equilibria. We find that harvesting destabilizes the system by inducing two saddle-node bifurcations. Notably, prey abundance can increase with greater Allee intensity under controlled harvesting-a rare and counterintuitive ecological outcome. Moreover, exceeding a critical harvesting threshold drives both species to extinction, while controlled harvesting allows sustainable coexistence. Numerical simulations support these analytical findings and identify critical parameter ranges for species coexistence. These results contribute to theoretical ecology and offer insights for designing sustainable harvesting strategies that balance exploitation with conservation.
Keyword ：
Allee effect Allee effect bifurcation bifurcation harvest harvest Lotka-Volterra commensal symbiosis model Lotka-Volterra commensal symbiosis model
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| GB/T 7714 | Fang, Kan , Wang, Yiqin , Chen, Fengde et al. Dynamics of a Modified Lotka-Volterra Commensalism System Incorporating Allee Effect and Symmetric Non-Selective Harvest [J]. | SYMMETRY-BASEL , 2025 , 17 (6) . |
| MLA | Fang, Kan et al. "Dynamics of a Modified Lotka-Volterra Commensalism System Incorporating Allee Effect and Symmetric Non-Selective Harvest" . | SYMMETRY-BASEL 17 . 6 (2025) . |
| APA | Fang, Kan , Wang, Yiqin , Chen, Fengde , Chen, Xiaoying . Dynamics of a Modified Lotka-Volterra Commensalism System Incorporating Allee Effect and Symmetric Non-Selective Harvest . | SYMMETRY-BASEL , 2025 , 17 (6) . |
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In this paper, we propose a discrete amensalism model incorporating cover and saturation effect. The discrete model is derived from its continuous counterpart using the piecewise constant parameter method. First, we determine the equilibria, outline the conditions for their existence, and analyze their local stability properties. Subsequently, by employing discrete equation deflation and iteration methods, we establish a set of sufficient conditions that ensure the global attractivity of the system. Our analysis demonstrates that the size of the cover and the natural growth rate of the second population significantly influence the global attractivity of the system. Next, we investigate the existence of both flip bifurcation and transcritical bifurcation near the positive and boundary equilibria under certain conditions, utilizing the central manifold theorem and bifurcation theory. To control chaos arising from flip bifurcation, we implement feedback control strategies, specifically the hybrid control method. Finally, numerical simulations verify the feasibility of our theoretical results. Our research reveals that both the presence of cover and saturation effect enhance the density of the first population, while an increase in the amensalism coefficient c1 ultimately leads to the extinction of the first population.
Keyword ：
chaos control chaos control cover cover flip bifurcation flip bifurcation global attractivity global attractivity Saturation effect Saturation effect tran-scritical bifurcation tran-scritical bifurcation
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| GB/T 7714 | Chong, Yanbo , Chen, Fengde . GLOBAL STABILITY, BIFURCATIONS AND CHAOS CONTROL IN A DISCRETE AMENSALISM MODEL WITH COVER AND SATURATION EFFECT [J]. | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION , 2025 , 15 (5) : 2977-3003 . |
| MLA | Chong, Yanbo et al. "GLOBAL STABILITY, BIFURCATIONS AND CHAOS CONTROL IN A DISCRETE AMENSALISM MODEL WITH COVER AND SATURATION EFFECT" . | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION 15 . 5 (2025) : 2977-3003 . |
| APA | Chong, Yanbo , Chen, Fengde . GLOBAL STABILITY, BIFURCATIONS AND CHAOS CONTROL IN A DISCRETE AMENSALISM MODEL WITH COVER AND SATURATION EFFECT . | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION , 2025 , 15 (5) , 2977-3003 . |
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