Competition in the gradostat: the global stability problem

DOI10.1016/0362-546X(94)90064-7zbMath0831.92027OpenAlexW2147682696MaRDI QIDQ4302398

Josef Hofbauer, Joseph W.-H. So

Publication date: 15 August 1994

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(94)90064-7

zbMATH Keywords

multiple stable equilibriageneral two vessel gradostatMonod growth functionsthree vessel gradostats

Mathematics Subject Classification ID

Ecology (92D40) Stability theory for ordinary differential equations (34D99)

Related Items (13)

Steady-state coexistence of three pure and simple competitors in a four- membered reactor network ⋮ Global stability for a model of competition in the chemostat with microbial inputs ⋮ Coexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates ⋮ The positive definiteness of a class of polynomials from the global stability analysis of Lotka-Volterra systems ⋮ The asymptotic behavior of a chemostat model with the Beddington-DeAngelis functional response. ⋮ Global behavior ofNcompeting species with strong diffusion: diffusion leads to exclusion ⋮ Nonlinear Evolution Equations and Applications ⋮ Coexistence of three microbial populations competing for three complementary nutrients in a chemostat ⋮ Oscillations of two competing microbial populations in configurations of two interconnected chemostats ⋮ Comparison of the global dynamics for two chemostat-like models: random temporal variation versus spatial heterogeneity ⋮ Competition in the periodic gradostat ⋮ On the coexistence of three microbial populations competing for two complementary substrates in configurations of interconnected chemostats ⋮ Global dynamics of the buffered chemostat for a general class of response functions

Cites Work

• Unnamed Item
• An index theorem for dissipative semiflows
• Mathematical investigations of growth of microorganisms in the gradostat
• Competition in the gradostat
• Stability and convergence in strongly monotone dynamical systems.
• On the Asymptotic Behavior of a Class of Deterministic Models of Cooperating Species
• Systems of Ordinary Differential Equations Which Generate an Order Preserving Flow. A Survey of Results
• Competition in an n-Vessel Gradostat
• Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations

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