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Convex dominates concave: An exclusion principle in discrete-time Kolmogorov systems
Author(s):
Ryusuke
Kon
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3025-3034.
MSC (2000):
Primary 92B05;
Secondary 39A11
Posted:
April 13, 2006
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Abstract:
We establish an exclusion principle in discrete-time Kolmogorov systems by using average Liapunov functions. The exclusion principle shows that a weakly dominant species with a convex logarithmic growth rate function eliminates species with concave logarithmic growth rate functions. A general result is applied to specific population models. This application gives an improved exclusion principle for the specific population models.
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Additional Information:
Ryusuke
Kon
Affiliation:
Faculty of Mathematics, Kyushu University, Hakozaki 6-10-1, Higashiku, Fukuoka 812-8581, Japan
Email:
kon-r@math.kyushu-u.ac.jp
DOI:
10.1090/S0002-9939-06-08309-2
PII:
S 0002-9939(06)08309-2
Keywords:
Exclusion principle,
dominance,
average Liapunov functions
Received by editor(s):
March 1, 2005
Received by editor(s) in revised form:
April 26, 2005
Posted:
April 13, 2006
Additional Notes:
The author was supported by the 21st Century COE Program ``Development of Dynamic Mathematics with High Functionality (Kyushu University)'' of the Ministry of Education, Culture, Sports, Science and Technology of Japan.
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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