Monotone bifurcation graphs

DOI10.1080/17513750701793873zbMath1141.92005OpenAlexW2133472643WikidataQ42716577 ScholiaQ42716577MaRDI QIDQ3520265

Germán A. Enciso, Eduardo D. Sontag

Publication date: 15 August 2008

Published in: Journal of Biological Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17513750701793873

zbMATH Keywords

reaction diffusion equationsdelay equationsgene regulatory networksmonotone systemsmultistabilityautoregulatory transcription network

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Dynamical systems in biology (37N25) Nonlinear systems in control theory (93C10) General biology and biomathematics (92B05) Monotone systems involving ordinary differential equations (34C12)

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Cites Work

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• The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
• Mathematical physiology
• Remarks on resolvent positive operators and their perturbation
• Multi-stability in monotone input/output systems
• On sets of Haar measure zero in abelian Polish groups
• Multistationarity, the basis of cell differentiation and memory. I. Structural conditions of multistationarity and other nontrivial behavior
• Bistability in cell signaling: How to make continuous processes discontinuous, and reversible processes irreversible
• Stability and convergence in strongly monotone dynamical systems.
• Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
• Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
• Monotone control systems
• A Small-Gain Theorem for Motone Systems With Multivalued Input-State Characteristics
• Stable coexistence and bi-stability for competitive systems on ordered Banach spaces