Stability and dynamical analysis of a biological system
type: Item
instance of: scholarly article
title: Stability and dynamical analysis of a biological system
zbMATH Open document ID: 1474.92135
DOI: 10.1155/2014/952840
author: Xinhong Pan
author: Min Zhao
author: Yapei Wang
author: Hengguo Yu
author: Zengling Ma
author: Qi Wang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This study considers the spatiotemporal dynamics of a reaction-diffusion phytoplankton-zooplankton system with a double Allee effect on prey under a homogeneous boundary condition. The qualitative properties are analyzed, including the local stability of all equilibria and the global asymptotic property of the unique positive equilibrium. We also discuss the Hopf bifurcation and the steady state bifurcation of the system. These results are expected to help understand the complexity of the Allee effect and the interaction between phytoplankton and zooplankton.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 7023384
Wikidata QID: Q59043073
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/952840
OpenAlex ID: W2042538388
cites work: Modeling the role of viral disease in recurrent phytoplankton blooms
cites work: Zooplankton mortality and the dynamical behaviour of plankton population models
cites work: Ocean plankton populations as excitable media
cites work: Global analysis in a predator-prey system with nonmonotonic functional response
cites work: Predator-prey system with strong Allee effect in prey
cites work: A delayed predator-prey model with strong Allee effect in prey population growth
cites work: A detailed study of the Beddington-DeAngelis predator-prey model
cites work: Existence of traveling wave solutions in a diffusive predator-prey model
cites work: Spatiotemporal Complexity of Plankton and Fish Dynamics
cites work: Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
cites work: MODELING FLUCTUATIONS IN A MINIMAL PLANKTON MODEL: ROLE OF SPATIAL HETEROGENEITY AND STOCHASTICITY
cites work: How predation can slow, stop or reverse a prey invasion
cites work: Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling
cites work: Dynamical analysis of a delayed reaction-diffusion predator-prey system
cites work: Consequences of double Allee effect on the number of limit cycles in a predator-prey model
cites work: Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect
cites work: Speeds of invasion in a model with strong or weak Allee effects
cites work: Multiple limit cycles in a Gause type predator-prey model with Holling type III functional response and Allee effect on prey
cites work: The stability of predator\,-\,prey systems subject to the Allee effects
cites work: The impact of Allee effect on a predator-prey system with Holling type II functional response
cites work: Geometric theory of semilinear parabolic equations
cites work: Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey
description: scientific article; zbMATH DE number 7023384