Dynamics of Lotka–Volterra Competition Systems with Large Interaction

By Edward Norman Dancer, Zhitao Zhang. 2002

61 citations recorded by the source corpus.

Abstract We show that under certain additional hypothesis, two population competing species models in bounded domains with diffusion and large interaction have simple dynamics. In particular, the solutions approach stationary states as t tends to infinity.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/7ecdaf57e94990f831f0813da9c958b743998c7e

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In Applied Mathematics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

Some new results in competing systems with many species (2010, methodology): “Then we give a uniform Lipschitz estimate, using Kato inequality (this inequality was also used in [10]) and our observation from the symmetric assumption bij = bji : Theorem 1.”
Strategy and stationary pattern in a three-species predator–prey model (2004, methodology): “These include the Gierer–Meinhardt model [14,18,39–41], the Sel’kov model [11,36], the Noyes–Field model for Belousov–Zhabotinskii reaction [31], the chemotactic diffusion model [21,38], the competition model [6,10,22–24], the predator–prey model [7,8,12,13,17,19,20,29,30,37], as well as models of s”
Saddle-point behavior for monotone semiflows and reaction–diffusion models☆ (2004, background): “, [9] and references therein), the study of uniqueness of positive steady states seems to be very difficult.”