Topological horseshoe and its uniform hyperbolicity in the HP model.

A famous food-chain model proposed by Hastings and Powell is numerically restudied. The existence and uniform hyperbolicity of chaotic invariant sets are demonstrated by means of the topological horseshoe theory and the Conley-Moser conditions, indicating that, for a fixed cross section, the second return Poincaré map of the model possesses a closed uniformly hyperbolic chaotic invariant set, on which it is topologically conjugate to the 2-shift map.