The theorem of the carrying simplex for competitive system defined on the n-rectangle and its application to a three-dimensional system

DOI10.1142/S1793524514500636zbMath1308.34064OpenAlexW2019312821WikidataQ62125457 ScholiaQ62125457MaRDI QIDQ5174397

Lei Niu, Ji-Fa Jiang

Publication date: 17 February 2015

Published in: International Journal of Biomathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793524514500636

zbMATH Keywords

limit cycleHopf bifurcationglobal attractorcompetitive systemcarrying simplexdynamical behaviorglobal phase portraitlinear structure saturation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25) Qualitative investigation and simulation of ordinary differential equation models (34C60) Asymptotic properties of solutions to ordinary differential equations (34D05) Attractors of solutions to ordinary differential equations (34D45) Monotone systems involving ordinary differential equations (34C12)

Related Items (3)

Convex geometry of the carrying simplex for the May-Leonard map ⋮ On global dynamics of type-K competitive Kolmogorov differential systems ⋮ On existence and uniqueness of a carrying simplex in Kolmogorov differential systems

Cites Work

• Stability by Liapunov's direct method. With applications
• Some mathematical problems concerning the ecological principle of competitive exclusion
• Limit cycles for the competitive three dimensional Lotka-Volterra system
• Periodic orbits of competitive and cooperative systems
• Dynamics of the periodic type-\(K\) competitive Kolmogorov systems
• Systems of differential equations which are competitive or cooperative: III. Competing species
• Invariant Structures in a System of Competitive Logistic Ordinary Differential Equations
• Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems
• The dynamical behaviour of type-K competitive Kolmogorov systems and its application to three-dimensional type-K competitive Lotka Volterra systems
• From local to global behavior in competitive Lotka-Volterra systems
• Geršgorin theorems by Householder’s proof

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