Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses

Alsakaji, Hebatallah J.; Kundu, Soumen; Rihan, Fathalla A.

doi:10.1016/j.amc.2020.125919

Cited by 41 publications

(21 citation statements)

References 31 publications

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“…The use of such an approach for floodplain wetland fauna could thus link the densitydependent dynamics of predator and prey populations [27] and help to understand direct and indirect food-web interactions [28,29] among key individuals (such as macroinvertebrates, freshwater fish and plants) in these systems. Previous studies on predator-prey interactions have mostly focused on MPE relationships between macroinvertebrate predators and their prey [30,31], however, higher trophic levels have lacked extensive examination (but see Wasserman et al [32] and Mofu et al [33]).…”

Section: Introductionmentioning

confidence: 99%

Functional Responses and Additive Multiple Predator Effects of Two Common Wetland Fish

Munyai

Dalu

Wasserman

et al. 2022

Water

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Understanding trophic interactions is essential for the prediction and measurement of structure and function in aquatic environments. Communities in these ecosystems may be shaped by variables such as predator diversity, prey density and emergent multiple predator effects (MPEs), which are likely to influence trophic dynamics. In this study, we examined the effect of key predatory fish in floodplain wetlands, namely Oreochromis mossambicus and Enteromius paludinosus, towards Chironomidae prey, using a comparative functional response (FR) approach. We used single predator species as well as intra- and interspecific paired species to contrast FRs under multiple predator scenarios. Attack rate and handling time estimates from single predator FRs were used to predict multiple predators’ feeding rates, which were compared to observe multiple predators’ feeding rates to quantify potential MPEs. From single fish trials, each species displayed a significant Type II FR, characterized by high feeding rates at low prey densities. Oreochromis mossambicus had a steeper (initial slope, i.e., higher attack rate) and higher (asymptote of curve, i.e., shorter handling time and higher maximum feeding rate) FR, whereas E. paludinosus exhibited lower-magnitude FRs (i.e., lower attack rate, longer handling time and lower feeding rate). In multiple predator scenarios, feeding rates were well-predicted by those of single predators, both in conspecific and interspecific pairs, and thus we did not find evidence for antagonistic or synergistic MPEs. Predator–prey interactions in wetland systems can have significant consequences on the structure and dynamics of ecological communities. In turn, this could have destabilizing effects on resources in tropical wetlands. These results, although experimental, help us understand how trophic interaction among conspecific or interspecific fish species in Austral tropical wetlands might influence their aquatic prey species. This will help us to understand food web dynamics better.

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Section: Introductionmentioning

confidence: 99%

Functional Responses and Additive Multiple Predator Effects of Two Common Wetland Fish

Munyai

Dalu

Wasserman

et al. 2022

Water

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“…From a mathematical point of view, models (1) and ( 2) also have some new interesting features that differ from previous models. Compared to the previous steady-state problems in [1,[10][11][12][13][14][15] and other related logistic population models with one nonlocal term (see e.g., [22][23][24][25][26][27][28][29][30][31]), the appearance of two nonlocal nonlinear terms in equation ( 1) will cause more mathematical difficulties and make the analysis of the model particularly interesting. Under certain new assumptions on g and K, our main result will be proved by using the fixed point index theory on cone.…”

Section: Introductionmentioning

confidence: 99%

Single Phytoplankton Species Growth with Nonlocal Crowding Effect Caused by Chemosensory Aggregation in a Water Column

Wang

Yao

2022

Complexity

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In this paper, we study the existence of positive steady states for a nonlocal reaction-diffusion model which describes the growth of a single phytoplankton species with nonlocal crowding effect caused by chemosensory aggregation in a water column. Our result shows that under some conditions, the nonlocal crowding effect is effective to the existence of steady states of phytoplankton populations. Based on a key boundedness Lemma, the main result is proved by fixed point index theory and some analytical techniques.

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“…Meanwhile, the food webs and food chains, including three or more species, comprise all components for the occurrence of chaos. This has encouraged several researchers to study the chaotic dynamics of an ecosystem [5,[16][17][18][19][20]. Naji and Balasim [21] considered a three-species food chain with the Beddington-DeAngelis response and obtained different stability conditions of the system.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

Noufaey¹,

Khaled²

2021

Symmetry

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In this study, the dynamics of a diffusive Lotka–Volterra three-species system with delays were explored. By employing the Galerkin Method, which generates semi-analytical solutions, a partial differential equation system was approximated through mathematical modeling with delay differential equations. Steady-state curves and Hopf bifurcation maps were created and discussed in detail. The effects of the growth rate of prey and the mortality rate of the predator and top predator on the system’s stability were demonstrated. Increase in the growth rate of prey destabilised the system, whilst increase in the mortality rate of predator and top predator stabilised it. The increase in the growth rate of prey likely allowed the occurrence of chaotic solutions in the system. Additionally, the effects of hunting and maturation delays of the species were examined. Small delay responses stabilised the system, whilst great delays destabilised it. Moreover, the effects of the diffusion coefficients of the species were investigated. Alteration of the diffusion coefficients rendered the system permanent or extinct.

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Delay differential model of one-predator two-prey system with Monod-Haldane and holling type II functional responses

Cited by 41 publications

References 31 publications

Functional Responses and Additive Multiple Predator Effects of Two Common Wetland Fish

Functional Responses and Additive Multiple Predator Effects of Two Common Wetland Fish

Single Phytoplankton Species Growth with Nonlocal Crowding Effect Caused by Chemosensory Aggregation in a Water Column

Stability Analysis of a Diffusive Three-Species Ecological System with Time Delays

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