For this system, how can we see that x(t) is the size of the prey population at any time t and y(t) is the number of predators at time t? First of all, note that if there are no predators—that is, if y is always 0—the system reduces to x˙=0.2x, y˙=0. This says ...
in which the population of one species (predators) has a negative effect on the population of a second (prey), while the second has a positive effect on the first. For population dynamics, predator-prey interactions are similar to other types of antagonistic interactions, such as pathogen-host...
Coefficient d measures the predation rate, g and h are the natural death rates of the predator and the prey, respectively. All the parameters in system (1) are positive constants. Based on this basic model, Fang and Wang [14] took into consideration the mobility of population individuals ...
Moreover, this kind of experimental data can contribute to unravelling complexities in theoretical approaches by earlier studies and ultimately promote understanding the effect of multiple predators on prey population regulation.doi:10.1016/j.baae.2013.08.004Panagiotis D. Lampropoulos...
Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of ...
Trendlines are drawn to aid the In Fig. 5, the light emission and mass-spectrometer data shown in b can be compared with the calculations shown in c, which shows the corresponding quantities of l and the negative integral of the prey population curve, as calculated from equation pair [2...
Some of these more general systems allow the predation rates, in our case the constants d and e, to depend on the size of the prey population x. While the conditions given for those more general systems for the persistence of both predators are not as critical as the one given in our ...
Discrete stage-structured prey and prey-predator models are considered. Regarding the former, we prove that the models at hand are permanent (i.e., the population will neither go extinct nor exhibit ...
The non-trivial nullcline of the prey species represents a curve which intersect positive x-axis at (r0−da,0), when it exists. Also the non-trivial predator nullcline of the system is a hyperbolic curve. When the birth rate of prey population is less than its death rate, the model ...
Of relevance is the impact of bringing alternative food to predators on the sustainability of both predator and focal prey population. One of the key biological features when another prey type is considered as additional food is known as apparent competition [34], [41]. This describes the ...