Population models with diffusion, strong Allee effect and constant yield harvesting

Abstract

We study the steady state distribution of reaction diffusion equations with strong Allee effect type growth and constant yield harvesting (semipositone) in heterogeneous bounded habitats. Assuming the exterior of the habitat is completely hostile, we establish existence results for positive solutions. We also establish a multiplicity result for the non-harvested case. We obtain our results via the method of sub-super solutions.

Stability and Bifurcation for a Single‐Species Model with Delay Weak Kernel and Constant Rate Harvesting

“…Population models with different harvesting strategies have been studied by scholars, for example, impulsive harvesting [38][39][40][41][42][43][44], constant rate harvesting [45][46][47][48], optimal harvesting strategy [49], linear harvesting [50,51], and nonlinear harvesting [52,53]. Volterra's model [24] and Cushing's model [25] can sufficiently describe the deterministic dynamical behaviors.…”

Complex Dynamics of Wetland Ecosystem with Nonlinear Harvesting: Application to Chilika Lake in Odisha, India

“…Upadhyay et al [2011] proposed a reaction-diffusion model to study the dynamics of phytoplankton-zooplankton system in which the consumption of phytoplankton species follows the Beddington-DeAngelis type of functional response and found that the instability observed in the model aquatic system is diffusion driven and fish predation acts as a regularizing factor. A population model with diffusion, strong Allee effect and constant yield of harvesting has been studied by Ali et al [2009]. Spatiotemporal complexity of a three-species ratio-dependent food chain model has been proposed by Rao [2014] and he observed the sequences of cold spots → stripespots mixtures → stripes → hot stripes-spots mixtures → hot spots → chaotic wave patterns.…”

Existence and Multiplicity of Positive Solutions to a Quasilinear Elliptic Equation with Strong Allee Effect Growth Rate

“…The existence, nonexistence and/or multiplicity of positive solutions to problem (P λ ) have been studied extensively in the literature; see, for example, [1,2,5,6,8,9,[11][12][13][14][15][17][18][19][20][21][22][23][24][25] and the references therein. In many previous studies, the nonlinear function f (x, s)/s p−1 was assumed to be nonincreasing in s, and under this condition, it can be shown that problem (P λ ) has at most one positive solution (see, e.g., [1,6,8,9,22]).…”