4. Monotone Dynamical Systems

By Morris W. Hirsch, Hal L. Smith. 2005

624 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5559a1a08d0e2dd214d3e23eb248bb41bea2ad7a

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Citations in the corpus

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].”
Convergence in monotone and uniformly stable skew-product semiflows with applications (2005, background): “20 and [42], Chapter 7), it follows that for every f A 1⁄2a; b C and ðm; k; gÞ A Hðd; l; f Þ, the parabolic problem 42 Jiang and Zhao, Monotone and uniformly stable s-p semiflows”
Dynamics of a two-dimensional system of rational difference equations of Leslie--Gower type (2011, background): “Competitive and cooperative systems have been investigated by many authors, see [2,3,5-19].”
Monotone Chemical Reaction Networks (2007, methodology): “The theory of monotone systems has been developed by Hirsch in a series of papers about two decades ago (see [12‐16]) and Smith’s excellent monograph [ 27 ] for a review.”
Global attractivity of the diffusive Nicholson blowflies equation with Neumann boundary condition: A non-monotone case☆ (2008, background): “Moreover, there exist M > 0 and w > 0 such that ‖T (t)‖ ≡ sup{ ‖T (t)φ‖ ‖φ‖ : φ ∈ C and φ = 0} Me for all t ∈R+ (see [20,21,27]).”
Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks (2008, background): “Related to the results presented here, besides the above cited works [1, 2, 9, 24, 25] we mention the monographs of Gopalsamy [5], Kuang [10] and Smith [21], the papers of He [8], Kuang [11, 12], Kuang and Smith [13], Saito and Takeuchi [20], So et al.”
SPATIAL DYNAMICS OF THE DIFFUSIVE LOGISTIC EQUATION WITH A SEDENTARY COMPARTMENT (2004, background): “Hence (17) is a cooperative system (off-diagonal elements of the Jacobian are positive, see [ 30 ]).”
Attractors of non-autonomous stochastic lattice systems in weighted spaces (2014, unknown): “, [25, 26, 40, 47, 53].”
Nicholson's blowflies differential equations revisited: Main results and open problems (2010, background): “Some modifications of conditions (11) and (13) were presented in [23] and [30].”
Monotone maps: A review (2005, background): “For related results see Hess [28], Matano [57], Poláčik [64], Smith [72, 75].”
Distributed control of positive systems (2011, background): “to positive systems is monotone systems, characterized by the property that a partial ordering of initial states is preserved. Such dynamical systems were studied in a series of papers by Hirsch [6], [7], showing that monotonicity under some additional assumptions implies convergence almost everywhe”
Separable Lyapunov functions for monotone systems: Constructions and limitations. (2015, background): “the seminal works by Hirsch [12, 13, 14, 16, 15, 17], the textbook [37], as well as the more recent review article [18].”
Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles ☆ (2008, background): “See [24] for a discussion and many basic theorems, as well as the recent excellent exposition [15].”