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The necessary and sufficient conditions for the existence of periodic orbits in a Lotka–Volterra system

✍ Scribed by Yuanshi Wang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
137 KB
Volume
284
Category
Article
ISSN
0022-247X

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✦ Synopsis

By extending Darboux method to three dimension, we present necessary and sufficient conditions for the existence of periodic orbits in three species Lotka-Volterra systems with the same intrinsic growth rates. Therefore, all the published sufficient or necessary conditions for the existence of periodic orbits of the system are included in our results. Furthermore, we prove the stability of periodic orbits. Hopf bifurcation is shown for the emergence of periodic orbits and new phenomenon is presented: at critical values, each equilibrium are surrounded by either equilibria or periodic orbits.

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