Uniqueness and stability of positive steady state solutions for a ratio-dependent predator-prey system with a crowding term in the prey equation
From MaRDI portal
Publication:892270
DOI10.1016/j.nonrwa.2015.02.005zbMath1327.35160OpenAlexW2002032679MaRDI QIDQ892270
Jianchen Zhang, Xian-zhong Zeng, Yong-geng Gu
Publication date: 18 November 2015
Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.nonrwa.2015.02.005
Stability in context of PDEs (35B35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial-boundary value problems for second-order parabolic systems (35K51)
Related Items (11)
Bifurcations in the diffusive Bazykin model ⋮ Uniform ultimate boundedness of solutions of predator-prey system with Michaelis-Menten functional response on time scales ⋮ Combined effects of the spatial heterogeneity and the functional response ⋮ Single phytoplankton species growth with light and crowding effect in a water column ⋮ Existence and uniqueness of the positive steady state solution for a Lotka-Volterra predator-prey model with a crowding term ⋮ Asymptotic behavior and stability of positive solutions to a spatially heterogeneous predator-prey system ⋮ Bifurcation branch and stability of stationary solutions of a predator–prey model ⋮ Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator-prey system with the crowing term and the weak growth ⋮ Effect of the protection zone on coexistence of the species for a ratio-dependent predator-prey model ⋮ Long-time behavior of a diffusive prey-predator system with Beddington-DeAngelis functional response in heterogeneous environment ⋮ Bifurcation and Turing pattern formation in a diffusive ratio-dependent predator-prey model with predator harvesting
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Persistence and the global dynamics of the positive solutions for a ratio dependent predator-prey system with a crowding term in the prey equation
- A new proof of anti-maximum principle via a bifurcation approach
- Superlinear indefinite systems: beyond Lotka-Volterra models
- A diffusive predator-prey model with a protection zone
- Global stability of the equilibrium of a diffusive Holling-Tanner prey-predator model
- Nonconstant positive steady states for a ratio-dependent predator-prey system with cross-diffusion
- An anti-maximum principle for second order elliptic operators
- First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs
- A priori bounds and multiple solutions for superlinear indefinite elliptic problems
- Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs
- Diffusion vs cross-diffusion: An elliptic approach
- On the fixed point index and multiple steady-state solutions of reaction- diffusion systems
- Realization of prescribed patterns in the competition model.
- Dynamics of parabolic equations: from classical solutions to metasolutions.
- The boundary blow-up rate of large solutions.
- Uniform anti-maximum principles
- Effects of a degeneracy in the competition model. II: Perturbation and dynamical behaviour
- On the indices of fixed points of mappings in cones and applications
- Uniqueness of the blow-up boundary solution of logistic equations with absorbtion.
- Asymptotics for the blow-up boundary solution of the logistic equation with absorption.
- A diffusive predator-prey model in heterogeneous environment
- Spatial patterns for population models in a heterogeneous environment
- Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equations
- Effect of cross-diffusion on the stationary problem of a diffusive competition model with a protection zone
- Effects of cross-diffusion and heterogeneous environment on positive steady states of a prey-predator system
- Global solution branches for positive mappings
- Bifurcation, perturbation of simple eigenvalues, and linearized stability
- A ratio-dependent predator-prey model with diffusion
- Asymptotic behavior and uniqueness results for boundary blow-up solutions.
- Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone
- Optimal uniqueness theorems and exact blow-up rates of large solutions
- Some global results for nonlinear eigenvalue problems
- Bifurcation from simple eigenvalues
- Positive steady states of a prey-predator model with diffusion and non-monotone conversion rate
- Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up
- Qualitative analysis on a diffusive and ratio-dependent predator-prey model
- BIFURCATION FROM SIMPLE EIGENVALUES AND EIGENVALUES OF GEOMETRIC MULTIPLICITY ONE
- EXISTENCE AND UNIQUENESS OF BLOW-UP SOLUTIONS FOR A CLASS OF LOGISTIC EQUATIONS
- Allee effect and bistability in a spatially heterogeneous predator-prey model
- Diffusive logistic equations with indefinite weights: population models in disrupted environments
- Remarks on sublinear elliptic equations
- On the Positive Solutions of Semilinear Equations Δu + λu - hu p = 0 on the Compact Manifolds
- The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
- Qualitative analysis of a ratio-dependent predator–prey system with diffusion
- Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations
- Coexistence States and Global Attractivity for Some Convective Diffusive Competing Species Models
- Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems.
- On the existence and numerical computation of classical and non-classical solutions for a family of elliptic boundary value problems
This page was built for publication: Uniqueness and stability of positive steady state solutions for a ratio-dependent predator-prey system with a crowding term in the prey equation
