Global Attractors and Steady States for Uniformly Persistent Dynamical Systems

By Pierre Magal, Xiao-Qiang Zhao. SIAM Journal on Mathematical Analysis, 2005

523 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/deb38ee351f7d152a4c4949cf3a52d8fdaa8c5bc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Feng-Bin Wang
2. Sergei S. Pilyugin
3. C. Browne
4. Sze-Bi Hsu
5. Horst R. Thieme
6. Arnaud Ducrot
7. Xiao-Qiang Zhao
8. Hal L. Smith

In Modeling and Simulation

1. Xiao-Qiang Zhao
2. Xingfu Zou
3. Feng-Bin Wang
4. Arnaud Ducrot
5. Hal L. Smith
6. Yu Huang
7. Sze-Bi Hsu
8. Horst R. Thieme

In Public Health, Environmental and Occupational Health

1. Xiao-Qiang Zhao
2. Xingfu Zou
3. Arnaud Ducrot
4. Feng-Bin Wang
5. Hal L. Smith
6. Yu Huang
7. Sze-Bi Hsu
8. Horst R. Thieme

Citations in the corpus

• Dynamics of a Periodically Pulsed Bio-Reactor Model With a Hydraulic Storage Zone (2011, methodology): “Next, we prove the solution maps associated with our systems are asymptotically compact on any bounded set and then conclude that the associated Poincaré map is κ-contracting and admits a global attractor under some appropriate conditions by using the results in [10].”
• Global dynamics of a PDE in-host viral model (2014, result): “Next, we can derive a condition under which, the semiflow associated with our systems is κ-contracting and thereby, conclude that the semiflow admits a connected global attractor using the results in [16] (see also [17]).”
• Dynamical Systems And Population Persistence (2016, result): “Newer results also appear in the recent paper by Magal and Zhao [158].”
• GLOBAL ANALYSIS OF AGE-STRUCTURED WITHIN-HOST VIRUS MODEL (2013, methodology): “We use results from Hale and Waltman [6] to prove uniform persistence and use results from Magal and Zhao [9] to establish existence of a compact global attractor, A0, contained inside the uniformly persistent set.”
• Spatial propagation for a two component reaction–diffusion system arising in population dynamics (2016, background): “However let us mention the works of Theime [27], Thieme and Zhao [29] and Fang and Zhao [13] (see also the references cited therein) for the study of the asymptotic speed of spread for integral equations, Fang et al [12] for delay lattice equations and Hsu and Zhao [17], Wang and Castillo-Chavez [32”