title: Intrinsic noise and two-dimensional maps: quasicycles, quasiperiodicity, and chaos.
abstract: We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit of large system sizes is shown to be very well-approximated by a Fokker-Planck-like equation, or equivalently by a set of stochastic difference equations. This formalism is applied to the specific case of two species: one predator species and its prey species. Quasicycles, stochastic cycles sustained and amplified by the demographic noise, previously found in continuous-time predator-prey models are shown to exist, and their behavior predicted from a linear noise analysis is shown to be in very good agreement with simulations. The effects of the noise on other attractors in the corresponding deterministic map, such as periodic cycles, quasiperiodicity, and chaos, are also investigated.
authors.affiliation: Theoretical Physics Division, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: César
authors.initials: C
authors.lastname: Parra-Rojas
authors.affiliation: Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze and INFN, via Sansone 1, IT 50019 Sesto Fiorentino, Italy.
authors.forename: Joseph D
authors.initials: JD
authors.lastname: Challenger
authors.affiliation: Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze and INFN, via Sansone 1, IT 50019 Sesto Fiorentino, Italy.
authors.forename: Duccio
authors.initials: D
authors.lastname: Fanelli
authors.affiliation: Theoretical Physics Division, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Alan J
authors.initials: AJ
authors.lastname: McKane
mesh_terms: D017711:Nonlinear Dynamics; D013057:Spectrum Analysis; D013269:Stochastic Processes; D013997:Time Factors