Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey

By Jinfeng Wang, Junping Shi, Junjie Wei. 2011

403 citations recorded by the source corpus.

Abstract The dynamics of a reaction–diffusion predator–prey system with strong Allee effect in the prey population is considered. Nonexistence of nonconstant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as nonconstant steady state solutions are studied. These results show that the impact of the Allee effect essentially increases the system spatiotemporal complexity.

Subfields: Computer Networks and Communications, Genetics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/6d5e7fbd18a2289848969da7c093fedbac777de1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Jinfeng Wang
2. Junping Shi
3. Junjie Wei
4. Boying Wu
5. Sainan Wu
6. Yongli Song
7. Rui Peng

In Genetics

1. Junping Shi
2. Jinfeng Wang
3. Boying Wu
4. Sainan Wu
5. Junjie Wei
6. Yongli Song
7. Yuan Lou
8. Shangjiang Guo

In Public Health, Environmental and Occupational Health

1. Jinfeng Wang
2. Junjie Wei
3. Junping Shi
4. Boying Wu
5. Sainan Wu
6. Yongli Song
7. Yuan Lou
8. Shangjiang Guo

Citations in the corpus

• Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ✩ (2016, background): “From [46], we know that the constant equilibrium (0, 0) is always locally asymptotically stable, or one can observe that for (5.”
• Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model (2015, neutral): “…criteria for the stability of homogeneous steady-state and derivation of appropriate conditions for the existence and/or non-existence of non-constant stationary states (Pang and Wang, 2003; Peng and Shi, 2009; Peng et al., 2008; Shi, 2002; Shi et al., 2010; Smoller, 1994; Wang et al., 2011).”
• Pattern Formation of the Attraction-Repulsion Keller-Segel System (2013, neutral): “to be the Hopf bifurcation curve (see [50]).”
• Global bifurcation analysis and pattern formation in homogeneous diffusive predator–prey systems (2016, background): “when 0 < λ < λ̄, there is a globally asymptotically stable periodic orbit if h1(u) = f ′(u)g(u)/[g(u) − g(λ)] is non-increasing in (0, λ) ∪ (λ, K), see [42]; 5.”