Abstract
The process of invasion is fundamental to the study of the dynamics of ecological and epidemiological systems. Quantitatively, a crucial measure of species' invasiveness is given by the rate at which it spreads into new open environments. The so-called "linear determinacy" conjecture equates full nonlinear model spread rates with the spread rates computed from linearized systems with the linearization carried out around the leading edge of the invasion. A survey that accounts for recent developments in the identification of conditions under which linear determinacy gives the "right" answer, particularly in the context of non-compact and non-cooperative systems, is the thrust of this contribution. Novel results that extend some of the research linked to some the contributions covered in this survey are also discussed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1419-1436 |
| Number of pages | 18 |
| Journal | Mathematical Biosciences and Engineering |
| Volume | 10 |
| Issue number | 5-6 |
| DOIs | |
| State | Published - Oct 2013 |
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Keywords
- Dispersal
- Ecology
- Integer difference integral equations
- Nonlinear reaction diffusion difference equations
- Population biology
ASJC Scopus subject areas
- Applied Mathematics
- Modeling and Simulation
- Computational Mathematics
- Agricultural and Biological Sciences(all)
- Medicine(all)
Cite this
Some recent developments on linear determinacy. / Castillo-Chavez, Carlos; Li, Bingtuan; Wang, Haiyan.
In: Mathematical Biosciences and Engineering, Vol. 10, No. 5-6, 10.2013, p. 1419-1436.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Some recent developments on linear determinacy
AU - Castillo-Chavez, Carlos
AU - Li, Bingtuan
AU - Wang, Haiyan
PY - 2013/10
Y1 - 2013/10
N2 - The process of invasion is fundamental to the study of the dynamics of ecological and epidemiological systems. Quantitatively, a crucial measure of species' invasiveness is given by the rate at which it spreads into new open environments. The so-called "linear determinacy" conjecture equates full nonlinear model spread rates with the spread rates computed from linearized systems with the linearization carried out around the leading edge of the invasion. A survey that accounts for recent developments in the identification of conditions under which linear determinacy gives the "right" answer, particularly in the context of non-compact and non-cooperative systems, is the thrust of this contribution. Novel results that extend some of the research linked to some the contributions covered in this survey are also discussed.
AB - The process of invasion is fundamental to the study of the dynamics of ecological and epidemiological systems. Quantitatively, a crucial measure of species' invasiveness is given by the rate at which it spreads into new open environments. The so-called "linear determinacy" conjecture equates full nonlinear model spread rates with the spread rates computed from linearized systems with the linearization carried out around the leading edge of the invasion. A survey that accounts for recent developments in the identification of conditions under which linear determinacy gives the "right" answer, particularly in the context of non-compact and non-cooperative systems, is the thrust of this contribution. Novel results that extend some of the research linked to some the contributions covered in this survey are also discussed.
KW - Dispersal
KW - Ecology
KW - Integer difference integral equations
KW - Nonlinear reaction diffusion difference equations
KW - Population biology
UR - http://www.scopus.com/inward/record.url?scp=84884485046&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84884485046&partnerID=8YFLogxK
U2 - 10.3934/mbe.2013.10.1419
DO - 10.3934/mbe.2013.10.1419
M3 - Article
C2 - 24245623
AN - SCOPUS:84884485046
VL - 10
SP - 1419
EP - 1436
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
SN - 1547-1063
IS - 5-6
ER -