On stationary patterns of a reaction–diffusion model with autocatalysis and saturation law

145 citations recorded by the source corpus.

How researchers see this paper

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

Global bifurcation analysis and pattern formation in homogeneous diffusive predator–prey systems (2016, methodology): “We use the powerful Leray–Schauder degree theory to prove the existence of nonconstant steady states as in [24,25,33,34,45].”
Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model (2015, unknown): “…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).”
Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩ (2009, background): “2), we recall the following maximum principle (see [32,38]):”
Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case (2009, background): “1 of [32], it is noted that (w∗, z∗) is non-degenerate in the sense that zero is not the eigenvalue of such linearized problem (but not locally linearly stable since ±i√θ is a pair of conjugate imaginary eigenvalues of this linearized problem).”
Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey (2011, unknown): “9), we recall the following maximum principle [38]: Lemma 3.”