Wave trains in a model of gypsy moth population dynamics

J. W. Wilder; D. A. Vasquez; I. Christie; J. J. Colbert

doi:10.1063/1.166102

Wave trains in a model of gypsy moth population dynamics

J. W. Wilder
, D. A. Vasquez
, I. Christie
, J. J. Colbert

West Virginia University
Indiana University Fort Wayne
United States Department of Agriculture

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	700-706
Number of pages	7
Journal	Chaos
Volume	5
Issue number	4
DOIs	https://doi.org/10.1063/1.166102
State	Published - 1995
Externally published	Yes

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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.",

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year = "1995",

doi = "10.1063/1.166102",

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T1 - Wave trains in a model of gypsy moth population dynamics

AU - Wilder, J. W.

AU - Vasquez, D. A.

AU - Christie, I.

AU - Colbert, J. J.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

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DO - 10.1063/1.166102

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SN - 1054-1500

VL - 5

SP - 700

EP - 706

JO - Chaos

JF - Chaos

IS - 4

ER -

Wave trains in a model of gypsy moth population dynamics

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