Monotone Dynamical Systems

By M. W. Hirsch, Hal L. Smith. 2013

548 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/dd66d8659bd3301bde65053d5e2c45947f097232

Citations in the corpus

• Dynamics of a reaction-diffusion-advection modelfor two competing species (2012, unknown): “By the theory of monotone dynamical system [15, 20, 21, 27, 29], this guarantees the existence of at least one stable coexistence state of (1).”
• Reaction-diffusion-advection models for the effects and evolution of dispersal (2013, unknown): “fact there is a well developed theory of monotone dynamical systems; see [79].”
• Separable Lyapunov functions for monotone systems: Constructions and limitations. (2015, unknown): “the seminal works by Hirsch [12, 13, 14, 16, 15, 17], the textbook [37], as well as the more recent review article [18].”
• Analysis of three species Lotka-Volterra food web models with omnivory (2015, unknown): “A monotone ecosystem whose interactions among n-species are all cooperative or competitive (n = 2) have been well studied in the past three decades thanks to the theory of monotone dynamical systems [9].”
• Periodic solutions for a non-monotone family of delayed differential equations with applications to Nicholson systems (2016, unknown): “3), in [7] the authors considered convenient auxiliary cooperative systems, and exploited results from the theory of monotone DDEs as in [24], to deduce the global asymptotic behavior of solutions.”