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 languageEnglish (US)
Pages (from-to)1419-1436
Number of pages18
JournalMathematical Biosciences and Engineering
Volume10
Issue number5-6
DOIs
StatePublished - Oct 2013

Fingerprint

Determinacy
Invasion
Nonlinear Dynamics
nonlinear models
Linearization
Equate
Ecosystem
Nonlinear Model
Research
Surveys and Questionnaires

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 journalArticle

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