TY - JOUR
T1 - Persistence and extinction in Lotka-Volterra reaction-diffusion equations
AU - Allen, Linda J.S.
N1 - Funding Information:
It is a pleasure to thank L. J. Gross and especiallyT . G. Hallam for their many helpfuls uggestionas nd commentsF. inancial supportw asp rovidedb y the U.S. EnvironmentalP rotection Agency under Grant No. R806726010.T his paper is based,i n part, on a Ph.D. dissertations ubmittedt o the Universityo f Tennessee.
PY - 1983/7
Y1 - 1983/7
N2 - This paper analyzes the persistence and extinction behavior of Lotka-Volterra reaction-diffusion equations for a patch-type environment. The system of equations is the discretized version of the familiar random-diffusion model ut=f(u)+Duxx. It is shown that diffusion can alter the persistence or extinction behavior of the Lotka-Volterra system. A competitive or predator-prey system can become extinct, whereas a mutualistic system can persist.
AB - This paper analyzes the persistence and extinction behavior of Lotka-Volterra reaction-diffusion equations for a patch-type environment. The system of equations is the discretized version of the familiar random-diffusion model ut=f(u)+Duxx. It is shown that diffusion can alter the persistence or extinction behavior of the Lotka-Volterra system. A competitive or predator-prey system can become extinct, whereas a mutualistic system can persist.
UR - http://www.scopus.com/inward/record.url?scp=0002339937&partnerID=8YFLogxK
U2 - 10.1016/0025-5564(83)90068-8
DO - 10.1016/0025-5564(83)90068-8
M3 - Article
AN - SCOPUS:0002339937
VL - 65
SP - 1
EP - 12
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 1
ER -