A note on symmetries on equations of population dynamics and stability conditions

Authors:
Yoshiteru Ishida
Affiliations:
Department of Knowledge-Based Information Engineering, Toyohashi University of Technology, Tempaku, Toyohashi, Japan
Venue:
KES'07/WIRN'07 Proceedings of the 11th international conference, KES 2007 and XVII Italian workshop on neural networks conference on Knowledge-based intelligent information and engineering systems: Part III
Year:
2007

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Abstract

For the equations of population dynamics, this note presents three symmetries: a coordinate symmetry, an additive symmetry and an exchange symmetry. Among them, additive symmetry is a new one that should be held in equations of population dynamics particularly those for quasispecies. The distinguishability between species is also stressed to obtain the stability condition of 2-dim Lotka-Volterra model that satisfies the additive symmetry.