Study of a Leslie–Gower-type tritrophic population model

A nonlinear splitting algorithm for systems of partial differential equations with self-diffusion

“…Maximum value that the per-capita rate can attain D 0 , D 1 Measure the level of protection provided by the environment to the prey b 2 Measure of the competition among prey, u D 2 Value of v at which its per capita removal rate becomes w 2 /2 D 3 Loss in r due to the lack of its favorite food, v c Growth rate of r via sexual reproduction d 4 The strength of the overcrowding term Table 1: List of parameters used in the three species food chain model. All these parameters are positive constants.…”

“…We define x to be the spatial coordinate vector in two dimensions. The parameters d 1 are assumed to be nonnegative and uniformly bounded on Ω. Appropriate boundary conditions are specified.…”

“…Here, we examine Dirichlet boundary conditions, however our analysis extends to the Neumann boundary condition case in a straight forward manner. The parameter definitions are given in Table 1: 1 Growth rate of prey u a 2 Measures the rate at which v dies out when there is no u to prey on and no r w…”

Controlling Chaotic Dynamics of a Continuous Ecological Model

“…Ayala [10] proved experimentally that two species of Drosophila could coexist upon a single limit resource. Ayala's experiment leads to a large body of work, which continuous to this day, see [1,2,6,8,[15][16][17][19][20][21][22][23][24][25]. Upadhyay [20] studied Rosenzweig-McArthur [18] model to investigate the existence of complex dynamical behavior in a food chain model involving Holling type IV functional response of the form wx d+x+x 2 /i and the effects of the intraspecific competition in the first level of the model is also studied.…”

Stability and Hopf Bifurcation of a Delay Eco‐epidemiological Model With Nonlinear Incidence Rate

“…Lafferty and Morris [25] quantified that the predation rates on infected prey may be 31 times higher compared to that on susceptible prey. Thus, we consider the case when the predator mainly eats the infected prey with Leslie-Gower ratiodependent schemes (Song and Li, [32]; Nindjin et al, [30]; Aziz-Alaoui and Daher Okiye, [2]; Hsu and Hwang, [19]; Aziz-Alaoui, [1]; Greenhalgh D. and Haque M., [11]). That is to say, the predator consumes the prey according to the ratio-dependent functional response and the predator grows logistically with intrinsic growth rate δ and carrying capacity proportional to the prey populations size I(t).…”