Hidden linearity in systems for competition with evolution in ecology and finance

In [J.C. Sprott, Competition with evolution in ecology and finance, Phys. Lett. A 325 (2004) 329–333] a variant of the multispecies Lotka–Volterra model was proposed in which species competing for fixed finite resources are replaced by a new randomly chosen species whenever they become extinct. We applied Lie group analysis to this system and found that it can be reduced to a linear equation if certain values are given to the parameters involved, which rules out any chaotic behavior in these instances. Also different routes to linearization are shown. © 2007 Elsevier Inc. All rights reserved