Global Analysis in a Predator-Prey System with Nonmonotonic Functional Response

By Dongmei Xiao, Shigui Ruan. SIAM Journal on Applied Mathematics, 2001

518 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/cc23f1c2ce81b25a8a8d1333c77c211c9a4cf2fe

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Citations in the corpus

Non‐Constant Positive Steady States of a Predator‐Prey System with Non‐Monotonic Functional Response and Diffusion (2004, methodology): “In [36], Ruan and Xiao used the logistic growth (1.”
Permanence for a delayed discrete ratio-dependent predator–prey system with Holling type functional response☆ (2004, methodology): “We refer to the monographs [10,16,21,24] for general delayed biological systems and to [18,22,23,25–27,30,31] for investigation on predator– prey systems.”
Dynamical behavior of an epidemic model with a nonlinear incidence rate (2003, methodology): “By the theorems in Bogdanov [1,2] and Takens [21] or Kuznetsov [15] (see also [20]), we obtain the following local representations of the bifurcation curves in a small neighborhood of the origin.”
On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay ⁄ (2009, unknown): “Recently, Ruan and Xiao [77] studied the dynamics of system (1.13) with τ = 0 and found that the model undergoes a series of bifurcations including saddle-node bifurcation, Hopf bifurcations, and homoclinic bifurcation.”
Pattern formation of a predator-prey system with Ivlev-type functional response (2008, background): “In population dynamics, a functional response g(u, v) of the predator to the prey density refers to the change in the density of prey attached per unit time per predator as the prey density changes (Ruan & Xiao, 2001).”
Bifurcations in a predator–prey system of Leslie type with generalized Holling type III functional response☆ (2014, background): “Predator–prey systems with nonmonotone functional response have been extensively studied by many authors (see Wolkowicz [38], Ruan and Xiao [32], Zhu, Campbell and Wolkowicz [45], Xiao and Zhu [43], Broer, Naudot and Roussarie [6], Lamontagne, Coutu and Rousseau [23], Etoua and Rousseau [13], and re”
Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-IV Functional Response (2004, methodology): “where for the biological implications refer to [7,9, 11 ,14] and to references therein.”
Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model (2012, background): “In the area of mathematical ecology, an adequate amount of thorough investigation is carried out by several researchers to study the local and global dynamical behavior of several predator-prey models within deterministic environment, see [5–17] and references cited therein.”
Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses (2007, result): “Other results about ratio-dependent functional response can be found in [11, 15–18].”