Bifurcation analysis of a spruce budworm model with diffusion and physiological structures

Dynamics in a diffusive predator-prey system with stage structure and strong allee effect

“…For a contradiction, suppose λ p = a+ib (a, b ∈ R, a ≥ 0) is one root of Eq. (23) with nonnegative real part, then there must exists an integer k such that λ p = a + ib is the root of the (k + 1)th equation in (23). Substituting λ p = a + ib into the (k + 1)th equation of (23), we have…”

“…Since the prey and predator always distribute inhomogeneously in different locations, the diffusion has been taken into considered in many ecological models (see [3,27,8,24]). Xu and Wei [23] considered a diffusive budworm model with a structured population model subjected to the Neumann boundary conditions as follows:…”

Entire solutions of the spruce budworm model

“…As t → +∞, these solutions converge to one of the positive roots of f (u) = 0. For some other results about budworm population dynamics, we refer to the papers [20][21][22][23].…”

Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

“…As is well known, since the spruce budworm population site model [1] has been proposed and was accepted by numerous scholars, during the last decade, spruce budworm population models have been extensively investigated both in theory and applications, such as for protection of spruce trees and development of a strategy for spruce budworm population control [1][2][3][4][5][6][7][8][9][10][11][12][13]. For example, in [2], the authors considered the following standard structured partial differential model of the budworm population:…”