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32 pages, 2225 KB  
Article
Harvesting Practices and Local Ecological Knowledge (LEK) of Bahamian Land Crabs: Bridging Gaps Between Traditional and Scientific Knowledge
by Iain J. McGaw, Michael T. McSweeney, William F. Bigelow, Kaitlyn T. Gaitor, Scott G. Seamone, Owen R. O’Shea, Nicholas D. Higgs, Candice Brittain and Michelle T. Kuenzi
Animals 2025, 15(20), 2941; https://doi.org/10.3390/ani15202941 (registering DOI) - 10 Oct 2025
Abstract
Three species of land crab occur in The Bahamas; these are an important source of protein and income for Bahamian islanders. The crab harvesters represent an important and largely untapped knowledge source. We conducted surveys on the Bahamian islands of Andros, New Providence, [...] Read more.
Three species of land crab occur in The Bahamas; these are an important source of protein and income for Bahamian islanders. The crab harvesters represent an important and largely untapped knowledge source. We conducted surveys on the Bahamian islands of Andros, New Providence, and Eleuthera to document crabbing practices and catalogue this local ecological knowledge (LEK) of land crabs. The survey primarily employed close-ended questions targeting land crab harvesters; we also recorded general feedback from open-ended questions. Crab collection was primarily for self-consumption. Catch rates varied among islands, and were the highest on Andros. There was a preference for white land crabs (Cardisoma guanhumi) on Andros, whereas on Eleuthera and New Providence, there was no preference for either white or black crabs (Gecarcinus ruricola). The majority of respondents reported a decline in white and black crab numbers, with land development and overharvesting being consistently cited factors. On Andros, forest fires were also reported to account for the loss of crab habitat, whereas on Eleuthera, invasive raccoons were blamed for the population decline. Respondents identified broadleaf forests as critical refuges and food sources for black crabs. Birds were the major predator, confirming findings for other land crab species. Land crabs were not merely a food resource but represented a complex nexus of ecological knowledge, economic systems, cultural traditions, and community practices within Bahamian society. We demonstrated a substantial overlap between traditional and scientific knowledge systems, providing valuable insights into land crab behaviour, habitat use, and ecology that complements formal scientific research. Full article
(This article belongs to the Section Human-Animal Interactions, Animal Behaviour and Emotion)
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22 pages, 1642 KB  
Article
Spatiotemporal Dynamics of a Predator–Prey Model with Harvest and Disease in Prey
by Jingen Yang, Zhong Zhao, Yingying Kong and Jing Xu
Mathematics 2025, 13(15), 2474; https://doi.org/10.3390/math13152474 - 31 Jul 2025
Viewed by 361
Abstract
In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability [...] Read more.
In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability method, and the conditions for Hopf bifurcation to occur near the positive equilibrium are investigated. The simulation results indicate that an increase in infection force might disrupt the stability of the model, while an increase in harvesting intensity would make the model stable. For the spatiotemporal model, a priori estimate for the positive steady state is obtained for the non-existence of the non-constant positive solution using maximum principle and Harnack inequality. The Leray–Schauder degree theory is used to study the sufficient conditions for the existence of non-constant positive steady states of the model, and pattern formation are achieved through numerical simulations. This indicates that the movement of prey and predators plays an important role in pattern formation, and different diffusions of these species may play essentially different effects. Full article
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16 pages, 2103 KB  
Article
Morinda citrifolia Essential Oil in the Control of Banana Anthracnose: Impacts on Phytotoxicity, Preventive and Curative Effects and Fruit Quality
by Maysa C. Santos, Luis O. Viteri, Paulo R. Fernandes, Rosilene C. Carvalho, Manuel A. Gonzalez, Osmany M. Herrera, Pedro R. Osório, Dalmarcia S. C. Mourão, Sabrina H. Araujo, Cristiano B. Moraes, Marcos V. Giongo, Wellington S. Moura, Marcos P. Camara, Alex Sander R. Cangussu, Raimundo W. S. Aguiar, Eugênio E. Oliveira and Gil R. Santos
Microbiol. Res. 2025, 16(7), 149; https://doi.org/10.3390/microbiolres16070149 - 3 Jul 2025
Viewed by 803
Abstract
Bananas, one of the most widely consumed tropical fruits in the world, are susceptible to attack by the anthracnose fungus Colletotrichum musae during the post-harvest period. Currently, fungus control is generally based on the use of chemical products, often applied a few days [...] Read more.
Bananas, one of the most widely consumed tropical fruits in the world, are susceptible to attack by the anthracnose fungus Colletotrichum musae during the post-harvest period. Currently, fungus control is generally based on the use of chemical products, often applied a few days before harvest, which could lead to a risk of residues in the fruit, thus creating a high demand for fresh and organic fruits. Therefore, essential oils present an emerging alternative for the treatment of anthracnose. Here, we evaluated the chemical composition and potential of Morinda citrifolia essential oil as a preventive and curative measure to control C. musae in bananas, also considering the quality of the fruit. In addition, computational docking analysis was conducted to predict potential molecular interactions between octanoic and butanoic acids and the enzyme Tyrosine tRNA, as a potential target for the M. citrifolia essential oil fungicide actions. We also evaluated the essential oil’s safety for beneficial organisms such as the fungus Trichoderma asperellum and the ladybugs Eriopis connexa Germar and Coleomegilla maculata DeGeer. Initially, in vitro growth inhibition tests were performed with doses of 10.0, 30.0, and 50.0 µL/mL of M. citrifolia essential oil, as well as an assessment of the phytotoxic effects on the fruit. Subsequently, using non-phytotoxic doses, we evaluated the effect of the essential oil as a preventive and curative measure against anthracnose and its impact on fruit quality. Our results showed that octanoic, butanoic, and hexanoic acids were the major compounds in M. citrifolia essential oil, inhibiting the growth of C. musae by interacting with the Tyrosine tRNA enzyme of C. musae. The non-phytotoxic dose on the fruit was 10 µL/mL of noni essential oil, which reduced C. musae growth by 30% when applied preventively and by approximately 25% when applied as a curative measure. This significantly reduced the Area Under the Disease Progress Curve without affecting the fruit weight, although there was a slight reduction in °Brix. The growth of non-target organisms, such as T. asperellum and the insect predators Co. maculata and E. connexa, was not affected. Collectively, our findings suggest that M. citrifolia essential oil is a promising alternative for the prevention and control of anthracnose in banana fruit caused by C. musae, without adversely affecting its organoleptic characteristics or non-target organisms. Full article
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24 pages, 427 KB  
Review
Ecology of Ahasverus advena in Stored Products and Other Habitats
by David W. Hagstrum and Bhadriraju Subramanyam
Insects 2025, 16(3), 313; https://doi.org/10.3390/insects16030313 - 18 Mar 2025
Viewed by 1292
Abstract
The foreign grain beetle, Ahasverus advena (Waltl) (Coleoptera: Silvanidae), has been reported from 110 countries on more than 162 commodities, more than 35 types of facilities, and 14 other habitats such as compost heaps and haystacks or manure. Compost heaps, haystacks, and manure [...] Read more.
The foreign grain beetle, Ahasverus advena (Waltl) (Coleoptera: Silvanidae), has been reported from 110 countries on more than 162 commodities, more than 35 types of facilities, and 14 other habitats such as compost heaps and haystacks or manure. Compost heaps, haystacks, and manure heated by fermentation may allow overwintering in cold climates, making them important sources of infestation. From these sources the A. advena can fly and infest grain storage and processing facilities. A. advena has been found in empty grain storage bins, is often found in wheat immediately after harvest, and is most abundant early in wheat storage. Larvae and adults of A. advena are well adapted to feeding on several species of fungi and have higher chitinase levels and greater tolerance for fungal aflatoxins than other species. A. advena lay more eggs on the fungal species on which their offspring can develop most successfully. They are attracted to fungal odors and high moisture commodities and have the capability to disseminate grain fungi that cause hot spots within the grain mass. The presence of fungus beetles is indicative of poor storage conditions. A. advena is capable of feeding on some commodities and is a predator that may have a potential role in biological control. They are strong fliers but are distributed extensively with the movement of commodities in the marketing system. In countries with a zero tolerance for insects, their presence is sufficient for rejection of a load and associated economic losses. In other countries, contamination by A. advena is a problem, and in India, it is listed as a quarantine pest. Extension agents have had many requests for the identification of this species, and two other species of the same genus have been found in stored products. Some information is available for the effectiveness of nine pest management methods for A. advena. Full article
(This article belongs to the Section Insect Pest and Vector Management)
18 pages, 8227 KB  
Article
Rice Stubble Provides Overwintering Microhabitats for Spiders in Winter-Fallowed Rice Fields
by Jie Sun, Xuhao Song, Jundong He, Dongmei Chen, Tingbang Yang and Aimin Shi
Agriculture 2025, 15(4), 381; https://doi.org/10.3390/agriculture15040381 - 11 Feb 2025
Viewed by 894
Abstract
Spiders are among the predominant predatory arthropods in rice field ecosystems. Although the potential of spiders for controlling pests during the growth stages of rice is well known, few studies have focused on the overwintering habits of spiders after rice harvesting. In the [...] Read more.
Spiders are among the predominant predatory arthropods in rice field ecosystems. Although the potential of spiders for controlling pests during the growth stages of rice is well known, few studies have focused on the overwintering habits of spiders after rice harvesting. In the present study, we aimed to evaluate the potential of rice stubble as an overwintering microhabitat for spiders in winter-fallowed rice fields. To this end, we investigated the arthropod community composition and analyzed the prey spectra of common predators in rice stubble in winter-fallowed rice fields in Nanchong City, Sichuan Province, China. The results showed that abundant predatory arthropods, particularly spiders, were present in the rice stubble, followed by other arthropods and pests. Dietary analysis via DNA metabarcoding revealed the prey availability and/or predation frequency of spiders is low in winter rice fields. Nevertheless, pests and other arthropods (particularly collembolans) within rice stubble serve as food resources for predators, particularly spiders, in winter-fallowed rice fields. Our results confirm that rice stubble provides overwintering microhabitats for spiders in winter-fallowed fields. Therefore, it is particularly important to properly manage rice stubble in winter-fallowed rice fields to enhance the biological pest control services of predators (including spiders). In addition, our findings highlight the potential of rice stubble as a habitat for the artificial reproduction of spiders for pest control in rice fields. Full article
(This article belongs to the Special Issue Advances in Biological Pest Control in Agroecosystems)
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33 pages, 3898 KB  
Article
Effects of Predation-Induced Emigration on a Landscape Ecological Model
by James T. Cronin, Nalin Fonseka, Jerome Goddard, Ratnasingham Shivaji and Xiaohuan Xue
Axioms 2025, 14(1), 63; https://doi.org/10.3390/axioms14010063 - 16 Jan 2025
Viewed by 825
Abstract
Predators impact prey populations directly through consumption and indirectly via trait-mediated effects like predator-induced emigration (PIE), where prey alter movement due to predation risk. While PIE can significantly influence prey dynamics, its combined effect with direct predation in fragmented habitats is underexplored. Habitat [...] Read more.
Predators impact prey populations directly through consumption and indirectly via trait-mediated effects like predator-induced emigration (PIE), where prey alter movement due to predation risk. While PIE can significantly influence prey dynamics, its combined effect with direct predation in fragmented habitats is underexplored. Habitat fragmentation reduces viable habitats and isolates populations, necessitating an understanding of these interactions for conservation. In this paper, we present a reaction–diffusion model to investigate prey persistence under both direct predation and PIE in fragmented landscapes. The model considers prey growing logistically within a bounded habitat patch surrounded by a hostile matrix. Prey move via unbiased random walks internally but exhibit biased movement at habitat boundaries influenced by predation risk. Predators are assumed constant, operating on a different timescale. We examine three predation functional responses—constant yield, Holling Type I, and Holling Type III—and three emigration patterns: density-independent, positive density-dependent, and negative density-dependent emigration. Using the method of sub- and supersolutions, we establish conditions for the existence and multiplicity of positive steady-state solutions. Numerical simulations in one-dimensional habitats further elucidate the structure of these solutions. Our findings demonstrate that the interplay between direct predation and PIE crucially affects prey persistence in fragmented habitats. Depending on the functional response and emigration pattern, PIE can either mitigate or amplify the impact of direct predation. This underscores the importance of incorporating both direct and indirect predation effects in ecological models to better predict species dynamics and inform conservation strategies in fragmented landscapes. Full article
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16 pages, 1861 KB  
Article
Dynamics of a Fractional-Order Eco-Epidemiological Model with Two Disease Strains in a Predator Population Incorporating Harvesting
by Moustafa El-Shahed and Mahmoud Moustafa
Axioms 2025, 14(1), 53; https://doi.org/10.3390/axioms14010053 - 11 Jan 2025
Cited by 3 | Viewed by 878
Abstract
In this paper, a fractional-order eco-epidemiological model with two disease strains in the predator population incorporating harvesting is formulated and analyzed. The model assumes that the population is divided into a prey population, a susceptible predator population, a predator population infected by the [...] Read more.
In this paper, a fractional-order eco-epidemiological model with two disease strains in the predator population incorporating harvesting is formulated and analyzed. The model assumes that the population is divided into a prey population, a susceptible predator population, a predator population infected by the first disease, and a predator population infected by the second disease. A mathematical analysis and numerical simulations are performed to explain the dynamics and properties of the proposed fractional-order eco-epidemiological model. The positivity, boundedness, existence, and uniqueness of the solutions are examined. The basic reproduction number and some sufficient conditions for the existence of four equilibrium points are obtained. In addition, some sufficient conditions are proposed to ensure the local and global asymptotic stability of the equilibrium points. Theoretical results are illustrated through numerical simulations, which also highlight the effect of the fractional order. Full article
(This article belongs to the Special Issue Advances in Dynamical Systems and Control)
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13 pages, 2125 KB  
Article
Effects of Cover Crops on Nematode Communities in Spinach Production
by Elyse Aubry, Jerry Akanwari, Ping Liang, Walid Ellouze, Jonathan Gaiero and Tahera Sultana
Int. J. Mol. Sci. 2024, 25(24), 13366; https://doi.org/10.3390/ijms252413366 - 13 Dec 2024
Cited by 1 | Viewed by 1190
Abstract
Agricultural soil environments contain different types of nematodes in all trophic levels that aid in balancing the soil food web. Beneficial free-living nematodes (FLNs) consist of bacterivores, fungivores, predators, and omnivores that help in the mineralization of the soil and the top-down control [...] Read more.
Agricultural soil environments contain different types of nematodes in all trophic levels that aid in balancing the soil food web. Beneficial free-living nematodes (FLNs) consist of bacterivores, fungivores, predators, and omnivores that help in the mineralization of the soil and the top-down control of harmful plant-parasitic nematodes (PPNs). Annually, USD 125 billion in worldwide crop losses are caused by PPNs, making them a plant pathogen of great concern for growers. Farmers have started to implement the use of cover crops in agricultural systems for the protection and enrichment of soil but research on how different cover crops affect nematode populations is lacking and in demand. This study aims to determine the effects of legume and grass cover crops, Cowpea (Vigna unguiculata) and Pearl Millet (Pennisetum glaucum), as well as their mixture on the abundance and diversity of FLN and PPN populations. Soil samples were collected at the time of cover crop maturity and spinach harvest to analyze nematode communities using both morphological and DNA metabarcoding analysis. The results showed that the application of Cowpea and Pearl Millet as well as their mixture in a spinach agricultural system led to the control of PPNs and proliferation of FLN communities, with each cover crop treatment demonstrating different advantages for the various nematode feeding groups. Soil property analysis did not show a significant difference except for magnesium and total nitrogen levels, which were significantly correlated with nematode community composition. The overall findings of our study indicate that the choice of cover crop implementation by growers for spinach cultivation should be based on specific soil health conditions, which in turn promote soil fertility and a healthy nematode community. Full article
(This article belongs to the Special Issue Interactions between Plants and Nematodes)
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12 pages, 1694 KB  
Article
Fan Mussel (Pinna nobilis L.) Spat Collection, Monitoring of Early Growth and Conservation Implications by Deploying Conventional Aquaculture Methodology
by John A. Theodorou, Efthimios Spinos, Alexis Ramfos, Ioannis E. Tsamadias, Vlasoula Bekiari, Maria Kamilari, Maria-Myrto Ntouni, Dimitrios Tsotsios, Konstantinos Feidantsis, Athanasios Lattos, Ioannis A. Giantsis and Basile Michaelidis
J. Mar. Sci. Eng. 2024, 12(11), 2070; https://doi.org/10.3390/jmse12112070 - 15 Nov 2024
Cited by 2 | Viewed by 1579
Abstract
Pinna nobilis, endemic to the Mediterranean Sea, has been experiencing a gradual population decline over recent decades due to anthropogenic pressures on its ecosystems. However, since 2016, its populations have suffered significant reductions because of pathological issues affecting the species across all its [...] Read more.
Pinna nobilis, endemic to the Mediterranean Sea, has been experiencing a gradual population decline over recent decades due to anthropogenic pressures on its ecosystems. However, since 2016, its populations have suffered significant reductions because of pathological issues affecting the species across all its habitats. Aquaculture techniques to support the limited natural recruitment P. nobilis efforts is examined. Artificial substrates for larval attachments in aquaculture infrastructures promote the survival of the juveniles that is further enhanced through protected pre-growing “nursery” farming conditions. Specific spat collectors were placed in 2 cage-fish farms in SW Amvrakikos Gulf. The harvested spats from were transferred to pre-grow in trays hanged on a long line farm mussel that is acting as a protected “nursery”, avoiding predation and any human accidentally disturbance. The survival and growth of 12 juveniles P. nobilis spat (shell length 38.1 ± 9.2 mm) in captivity (31 October 2023–15 March2023) was investigated. Out of the 12 individuals collected, 3 were examined for the presence of pathogens; only 7 survived, exhibiting enhanced growth (shell length 54.3 ± 11.6 mm) after 134 days in the nursery. The results highlight the significant role of aquaculture techniques in efforts to conserve a threatened species as well as the need for the creation of a protocol to ensure the conservation of P. nobilis. Full article
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28 pages, 11701 KB  
Article
Bifurcation of a Leslie–Gower Predator–Prey Model with Nonlinear Harvesting and a Generalist Predator
by Mengxin He and Zhong Li
Axioms 2024, 13(10), 704; https://doi.org/10.3390/axioms13100704 - 12 Oct 2024
Cited by 2 | Viewed by 1438
Abstract
A Leslie–Gower predator–prey model with nonlinear harvesting and a generalist predator is considered in this paper. It is shown that the degenerate positive equilibrium of the system is a cusp of codimension up to 4, and the system admits the cusp-type degenerate Bogdanov–Takens [...] Read more.
A Leslie–Gower predator–prey model with nonlinear harvesting and a generalist predator is considered in this paper. It is shown that the degenerate positive equilibrium of the system is a cusp of codimension up to 4, and the system admits the cusp-type degenerate Bogdanov–Takens bifurcation of codimension 4. Moreover, the system has a weak focus of at least order 3 and can undergo degenerate Hopf bifurcation of codimension 3. We verify, through numerical simulations, that the system admits three different stable states, such as a stable fixed point and three limit cycles (the middle one is unstable), or two stable fixed points and two limit cycles. Our results reveal that nonlinear harvesting and a generalist predator can lead to richer dynamics and bifurcations (such as three limit cycles or tristability); specifically, harvesting can cause the extinction of prey, but a generalist predator provides some protection for the predator in the absence of prey. Full article
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25 pages, 2125 KB  
Article
Dynamic Analysis and Optimal Control of a Fractional Order Fishery Model with Refuge and Protected Area
by Wenjun Gao, Xiu Jia and Ruiqing Shi
Axioms 2024, 13(9), 642; https://doi.org/10.3390/axioms13090642 - 19 Sep 2024
Cited by 1 | Viewed by 1130
Abstract
In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to [...] Read more.
In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to analyze predator-prey dynamics in a fishery model through the application of fractional derivatives. It is worth emphasizing that we explicitly examine how fractional derivatives affect the dynamics of the model. The existence of each equilibrium point and the stability of the system at the equilibrium point are proved. The theoretical results are proved by numerical simulation. Alternatively, allocate harvesting efforts within an improved model aimed at maximizing economic benefits and ecologically sustainable development. The ideal solution is obtained by applying Pontryagin’s optimal control principle. A large number of numerical simulations show that the optimal control scheme can realize the sustainable development of the ecosystem. Full article
(This article belongs to the Special Issue Mathematical Modeling, Simulations and Applications)
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44 pages, 7453 KB  
Article
Some Bifurcations of Codimensions 1 and 2 in a Discrete Predator–Prey Model with Non-Linear Harvesting
by Ming Liu, Linyi Ma and Dongpo Hu
Mathematics 2024, 12(18), 2872; https://doi.org/10.3390/math12182872 - 14 Sep 2024
Cited by 2 | Viewed by 1418
Abstract
This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension [...] Read more.
This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model. Full article
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21 pages, 21669 KB  
Article
Dynamics of a Predator–Prey System with Impulsive Stocking Prey and Nonlinear Harvesting Predator at Different Moments
by Zeli Zhou, Jianjun Jiao, Xiangjun Dai and Lin Wu
Mathematics 2024, 12(15), 2369; https://doi.org/10.3390/math12152369 - 30 Jul 2024
Cited by 1 | Viewed by 1452
Abstract
In this article, we study a predator–prey system, which includes impulsive stocking prey and a nonlinear harvesting predator at different moments. Firstly, we derive a sufficient condition of the global asymptotical stability of the predator–extinction periodic solution utilizing the comparison theorem of the [...] Read more.
In this article, we study a predator–prey system, which includes impulsive stocking prey and a nonlinear harvesting predator at different moments. Firstly, we derive a sufficient condition of the global asymptotical stability of the predator–extinction periodic solution utilizing the comparison theorem of the impulsive differential equations and the Floquet theory. Secondly, the condition, which is to maintain the permanence of the system, is derived. Finally, some numerical simulations are displayed to examine our theoretical results and research the effect of several important parameters for the investigated system, which shows that the period of the impulse control and impulsive perturbations of the stocking prey and nonlinear harvesting predator have a significant impact on the behavioral dynamics of the system. The results of this paper give a reliable tactical basis for actual biological resource management. Full article
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25 pages, 4246 KB  
Article
Investigating the Dynamic Behavior of Integer and Noninteger Order System of Predation with Holling’s Response
by Kolade M. Owolabi, Sonal Jain and Edson Pindza
Mathematics 2024, 12(10), 1530; https://doi.org/10.3390/math12101530 - 14 May 2024
Cited by 4 | Viewed by 1634
Abstract
The paper’s primary objective is to examine the dynamic behavior of an integer and noninteger predator–prey system with a Holling type IV functional response in the Caputo sense. Our focus is on understanding how harvesting influences the stability, equilibria, bifurcations, and limit cycles [...] Read more.
The paper’s primary objective is to examine the dynamic behavior of an integer and noninteger predator–prey system with a Holling type IV functional response in the Caputo sense. Our focus is on understanding how harvesting influences the stability, equilibria, bifurcations, and limit cycles within this system. We employ qualitative and quantitative analysis methods rooted in bifurcation theory, dynamical theory, and numerical simulation. We also delve into studying the boundedness of solutions and investigating the stability and existence of equilibrium points within the system. Leveraging Sotomayor’s theorem, we establish the presence of both the saddle-node and transcritical bifurcations. The analysis of the Hopf bifurcation is carried out using the normal form theorem. The model under consideration is extended to the fractional reaction–diffusion model which captures non-local and long-range effects more accurately than integer-order derivatives. This makes fractional reaction–diffusion systems suitable for modeling phenomena with anomalous diffusion or memory effects, improving the fidelity of simulations in turn. An adaptable numerical technique for solving this class of differential equations is also suggested. Through simulation results, we observe that one of the Lyapunov exponents has a negative value, indicating the potential for the emergence of a stable-limit cycle via bifurcation as well as chaotic and complex spatiotemporal distributions. We supplement our analytical investigations with numerical simulations to provide a comprehensive understanding of the system’s behavior. It was discovered that both the prey and predator populations will continue to coexist and be permanent, regardless of the choice of fractional parameter. Full article
(This article belongs to the Special Issue Numerical Solution of Differential Equations and Their Applications)
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8 pages, 578 KB  
Proceeding Paper
A Diseased Three-Species Harvesting Food Web Model with Various Response Functions
by Thangavel Megala, Thangaraj Nandha Gopal, Manickasundaram Siva Pradeep and Arunachalam Yasotha
Biol. Life Sci. Forum 2024, 30(1), 17; https://doi.org/10.3390/IOCAG2023-16876 - 11 Mar 2024
Cited by 2 | Viewed by 1008
Abstract
The purpose of this work is to present a three-species harvesting food web model that takes into account the interactions of susceptible prey, infected prey, and predator species. Prey species are assumed to expand logistically in the absence of predator species. The Crowley–Martin [...] Read more.
The purpose of this work is to present a three-species harvesting food web model that takes into account the interactions of susceptible prey, infected prey, and predator species. Prey species are assumed to expand logistically in the absence of predator species. The Crowley–Martin and Beddington–DeAngelis functional responses are used by predators to consume both susceptible and infected prey. Additionally, susceptible prey is consumed by infected prey in the formation of a Holling type II response. Both prey species are considered when prey harvesting is taken into account. Boundedness, positivity, and positive invariance are considered in this study. The investigation covers all the equilibrium points that are biologically feasible. Local stability is evaluated by analyzing the distribution of eigen values, while global stability is evaluated using suitable Lyapunov functions. Also, Hopf bifurcation is analyzed at the harvesting rate H1. At the end, we evaluate the numerical solutions based on our findings. Full article
(This article belongs to the Proceedings of The 2nd International Online Conference on Agriculture)
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