Applied Mathematical Ecology

1989 ◽  
Keyword(s):  
Mathematical Ecology

Mathematical ecology. An introduction

1988 ◽  
Vol 41 (1-2) ◽  
pp. 151-153
Author(s):  
Yuri M. Svirezhev
Keyword(s):  
Mathematical Ecology

An Introduction to Mathematical Ecology.

1975 ◽  
Vol 82 (9) ◽  
pp. 951
Author(s):  
Thomas Rogers ◽  
E. C. Pielou
Keyword(s):  
Mathematical Ecology

Divergent population processes and mammal outbreaks

1967 ◽  
Vol 4 (01) ◽  
pp. 1-8 ◽  
Author(s):  
P. Holgate
Keyword(s):  
Infinite System ◽  
Transition Probabilities ◽  
Positive Probability ◽  
System Of Differential Equations ◽  
Mathematical Ecology ◽  
Birth And Death Processes ◽  
Sample Paths ◽  
Image Position ◽  
Birth Processes ◽  
Necessary And Sufficient

Birth and death processes, i.e. Markov chains {X(t)}, 0 ≦ t ≦ ∞, taking values in the set I of non-negative integers, for which the infinitesimal transition probabilities are have found wide application in mathematical ecology . In order that the infinite system of differential Equations (1) should have solutions such that Pij (t) ≦ 0, all t and it is necessary and sufficient that . The conditions ensure that with probability one, the sample paths of X(t) have no discontinuities worse than jumps, and in this case the solution is unique. If (3) does not hold then for some t 1 at least, there is a set of sample paths of positive probability, each of which has t 1 as a limit point of jumps. For pure birth processes, (in which μj = 0) this clearly implies X(t) → ∞ as t → t 1.

Applied mathematical ecology

1990 ◽  
Vol 5 (11) ◽  
pp. 386
Author(s):  
Brian Grenfell
Keyword(s):  
Mathematical Ecology
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