title: Wave trains in a model of gypsy moth population dynamics.
abstract: A recent model of gypsy moth [Lymantria dispar (Lepidoptera: Lymantriidae)] populations led to the observation of traveling waves in a one-dimensional spatial model. In this work, these waves are studied in more detail and their nature investigated. It was observed that when there are no spatial effects the model behaves chaotically under certain conditions. Under the same conditions, when diffusion is allowed, traveling waves develop. The biomass densities involved in the model, when examined at one point in the spatial domain, are found to correspond to a limit cycle lying on the surface of the chaotic attractor of the spatially homogeneous model. Also observed are wave trains that have modulating maxima, and which when examined at one point in the spatial domain show a quasiperiodic temporal behavior. This complex behavior is determined to be due to the interaction of the traveling wave and the chaotic background dynamics. (c) 1995 American Institute of Physics.
authors.affiliation: Department of Mathematics, West Virginia University, P.O. Box 6310, Morgantown, West Virginia 26506Department of Physics, Indiana University-Purdue University, Fort Wayne, Fort Wayne, Indiana 46805Department of Mathematics, West Virginia University, P.O. Box 6310, Morgantown, West Virginia 26506USDA Forest Service, Northeastern Forest Experiment Station, P.O. Box 4360, Morgantown, West Virginia 26505.
authors.forename: J. W.
authors.initials: JW
authors.lastname: Wilder
authors.forename: D. A.
authors.initials: DA
authors.lastname: Vasquez
authors.forename: I.
authors.initials: I
authors.lastname: Christie
authors.forename: J. J.
authors.initials: JJ
authors.lastname: Colbert