Mutual exclusion versus coexistence for discrete competitive systems

DOI10.1007/BF00160333zbMath0735.92023OpenAlexW2027020228MaRDI QIDQ1180356

Publication date: 27 June 1992

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00160333

zbMATH Keywords

chaos extinction Lyapunov functions coexistence exponential rational omega-limit sets exclusion principle density dependent growth functions 2-species model discrete competition models

Mathematics Subject Classification ID

Ecology (92D40) Additive difference equations (39A10)

Related Items (67)

Simple dynamics in non-monotone Kolmogorov systems ⋮ Planting and harvesting for pioneer-climax models ⋮ Pre-images of invariant sets of a discrete-time two-species competition model ⋮ Pioneer exclusion in a one-hump discrete pioneer-climax competitive system ⋮ Two-patch dispersal-linked compensatory-overcompensatory spatially discrete population models ⋮ Species extinction using geometry of level surfaces ⋮ Constant and periodic rate stocking and harvesting for Kolmogorov-type population interaction models ⋮ Permanence and global attractivity of a discrete multispecies Lotka-Volterra competition pred\-a\-tor-prey systems ⋮ Prey dominance in discrete predator-prey systems with a prey refuge ⋮ Extinction of species in age-structured, discrete noncooperative systems ⋮ Bifurcation and global dynamics of a Leslie-Gower type competitive system of rational difference equations with quadratic terms ⋮ Lumped-density population models of pioneer-climax type and stability analysis of Hopf bifurcations ⋮ Hopf bifurcation in pioneer-climax competing species models ⋮ Hopf bifurcations in 3D competitive system with mixing exponential and rational growth rates ⋮ Quasi-uniformly asymptotic stability and existence of almost periodic solutions of difference equations with applications in population dynamic systemsThis work was supported by the National natural science foundation of China under grant (No.10671127) and Shanghai outstanding discipline leader project (No. 06XD14034) and Shanghai municipal education commission No. 06DZ002. ⋮ Global behavior of a two-dimensional competitive system of difference equations with stocking ⋮ Adaptive delayed reproduction in a 2-dimensional discrete-time competition model ⋮ Global dynamics of modified discrete Lotka-Volterra model ⋮ On the exponentially self-regulating population model ⋮ PERIOD-DOUBLING BIFURCATIONS FOR SYSTEMS OF DIFFERENCE EQUATIONS AND APPLICATIONS TO MODELS IN POPULATION BIOLOGY ⋮ Unnamed Item ⋮ Basins of attraction for two-species competitive model with quadratic terms and the singular Allee effect ⋮ On a system of rational difference equations ⋮ Probabilities of extinction, weak extinction permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems ⋮ Weak Allee effects and species coexistence ⋮ On a system of rational difference equations ⋮ Analysis of Coexistence and Extinction in a Two-Species Competition Model ⋮ Global dynamics of a discrete two-species Lottery-Ricker competition model ⋮ Principles of competitive exclusion for discrete populations with reproducing juveniles and adults ⋮ Exclusion and dominance in discrete population models via the carrying simplex ⋮ Asymptotic behavior of a competitive system of linear fractional difference equations ⋮ Dynamics of a two-dimensional competitive system of rational difference equations with quadratic terms ⋮ Two species competitive model with the allee effect ⋮ Global dynamics of a competitive system of rational difference equations in the plane ⋮ Multiple extinctions in a discrete competitive system ⋮ Some Discrete Competition Models and the Competitive Exclusion Principle^† ⋮ Geometry of exclusion principles in discrete systems ⋮ Stable periodic solution of the discrete periodic Leslie-Gower predator-prey model ⋮ Dynamics with riddled basins of attraction in models of interacting populations ⋮ Probabilities of extinction, weak extinction, permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems that involve invading species ⋮ Global stability of discrete competition model ⋮ Attractor information for discrete dynamical systems by means of optimal discrete Galerkin bases ⋮ Global stability of discrete population models with time delays and fluctuating environment ⋮ Asymptotic stability for difference equations with decreasing arguments ⋮ INVARIANT MANIFOLDS FOR COMPETITIVE DISCRETE SYSTEMS IN THE PLANE ⋮ Dynamics of a pioneer-climax species model with migration ⋮ Global attractors in competitive systems ⋮ Open problems and conjectures ⋮ On the population model of the non-autonomous logistic equation of second order with period-two parameters ⋮ Multiple attractors via CUSP bifurcation in periodically varying environments ⋮ Discrete hierarchical competition with reward and cost of dispersion ⋮ The effects of planting and harvesting on endangered species in discrete competitive systems ⋮ Permanence and universal classification of discrete-time competitive systems via the carrying simplex ⋮ Rational systems in the planeEdited by Gerry LadasIn this section, we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas: gladas@math.uri.edu ⋮ Bifurcation and invariant manifolds of the logistic competition model ⋮ Global behavior of four competitive rational systems of difference equations in the plane ⋮ Global dynamics of discrete competitive models with large intrinsic growth rates ⋮ Using stocking or harvesting to reverse period-doubling bifurcations in discrete population models ⋮ Geometric method for global stability of discrete population models ⋮ Global behavior of a three-dimensional linear fractional system of difference equations ⋮ Co-invasion waves in a reaction diffusion model for competing pioneer and climax species ⋮ Global dynamics of an anti-competitive system of rational difference equations in the plane ⋮ Global asymptotic behavior of a two-dimensional difference equation modelling competition ⋮ Bifurcation and chaos in discrete\,-\,time predator\,-\,prey system ⋮ A coupled system of rational difference equations ⋮ Extinction in discrete, competitive, multi-species patch models ⋮ Global Stability of Cycles: Lotka-Volterra Competition Model With Stocking

Cites Work

This page was built for publication: Mutual exclusion versus coexistence for discrete competitive systems