Results 251 to 260 of about 126,952 (298)
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1994
In the ecological models of the previous chapters much attention is given to the dynamics of a single population. In contrast, in this chapter we concentrate on the dynamics of interspecies interactions. The two-species model consists of a predator population and a prey population. Both are present within a given area with a specified carrying capacity.
Bruce Hannon, Matthias Ruth
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In the ecological models of the previous chapters much attention is given to the dynamics of a single population. In contrast, in this chapter we concentrate on the dynamics of interspecies interactions. The two-species model consists of a predator population and a prey population. Both are present within a given area with a specified carrying capacity.
Bruce Hannon, Matthias Ruth
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DYNAMICS OF MODIFIED PREDATOR-PREY MODELS
International Journal of Bifurcation and Chaos, 2010Besides being structurally unstable, the Lotka–Volterra predator-prey model has another shortcoming due to the invalidity of the principle of mass action when the populations are very small. This leads to extremely large populations recovering from unrealistically small ones.
Kloeden, P. E., Pötzsche, C.
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2003
When species interact the population dynamics of each species is affected. In general, there is a whole web of interacting species, called trophic web, which makes for structurally complex communities We consider here systems involving two species. There are three main types of interaction: (i) When the growth rate of one population is decreased,
Anatoly Swishchuk, Jianhong Wu
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When species interact the population dynamics of each species is affected. In general, there is a whole web of interacting species, called trophic web, which makes for structurally complex communities We consider here systems involving two species. There are three main types of interaction: (i) When the growth rate of one population is decreased,
Anatoly Swishchuk, Jianhong Wu
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A Discrete Predator-Prey Ecoepidemic Model
Mathematical Modelling of Natural Phenomena, 2017Summary: In this work we present a discrete predator-prey ecoepidemic model. The predator-prey interactions are represented by a discrete Leslie-Gower model with prey intra-specific competition. The disease dynamics follows a discrete SIS epidemic model with frequency-dependent transmission.
Bravo de la Parra, Rafael +3 more
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Dynamics of a Predator-Prey Model
SIAM Journal on Applied Mathematics, 1999Summary: We describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator-prey model proposed by \textit{R.M. May} [ Stability and complexity in model ecosystems. (1974)]. In particular, we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle ...
Sáez, E., González-Olivares, E.
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Predator—Prey Models of Fisheries
1997In another form of renewable resource depletion models, we use a biological predator–prey model with the economics of an optimal use path. We find that over the long run, the fishery rises and collapses repeatedly over the long term. We change the model to accommodate the concept of capital turnover costs.
Matthias Ruth, Bruce Hannon
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The hydra effect in predator–prey models
Journal of Mathematical Biology, 2011The seemingly paradoxical increase of a species population size in response to an increase in its mortality rate has been observed in several continuous-time and discrete-time models. This phenomenon has been termed the "hydra effect". In light of the fact that there is almost no empirical evidence yet for hydra effects in natural and laboratory ...
Sieber, Michael, Hilker, Frank M.
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A Two-Patch Predator-Prey Metapopulation Model
East Asian Journal on Applied Mathematics, 2012AbstractA minimal model for predator-prey interaction in a composite environment is presented and analysed. We first consider free migrations between two patches for both interacting populations, and then the particular cases where only one-directional migration is allowed and where only one of the two populations can migrate.
G. Quaglia +3 more
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Extinction probabilities in predator–prey models
Journal of Applied Probability, 1986Two stochastic models are developed for the predator-prey process. In each case it is shown that ultimate extinction of one of the two populations is certain to occur in finite time. For each model an exact expression is derived for the probability that the predators eventually become extinct when the prey birth rate is 0.
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On Lotka–Volterra predator prey models
Journal of Applied Probability, 1977Ever since Lotka (1925) and Volterra (1926), (1931) first considered mathematical formulations for prey-predator processes, the resultant equations have resisted attempts to solve them. However, over the intervening 50 years, standard techniques have allowed a few isolated results to be obtained for some simplified versions of the original process, but
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