Topological horseshoe and its uniform hyperbolicity in the HP model (Q2014351)

This paper considers a food chain model proposed by \textit{A. Hastings} and \textit{T. Powell} [``Chaos in a three-species food chain'', Ecology 72, No. 3, 896--903 (1991; \url{doi:10.2307/1940591})], consisting of three first-order nonlinear ODEs. The authors fix parameter values, choose a Poincaré section in the flow and investigate the second return map on this section. Using topological horseshoe theories and the Conley-Moser conditions, they use computations to show the existence of a hyperbolic chaotic invariant set, on which the second return map is topologically conjugate to the 2-shift map.