Vol. 10, No. 5, 2017

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Numerical existence and stability of solutions to the distributed spruce budworm model

Hala Al-Khalil, Catherine Brennan, Robert Decker, Aslihan Demirkaya and Jamie Nagode

Vol. 10 (2017), No. 5, 857–879
Abstract

This paper presents the steady-state solutions and traveling wave solutions for a spatially distributed PDE version of the spruce budworm model. The ODE (undistributed) model has been used in practical scenarios to model the outbreaks of the spruce budworm in forest environments, alongside the study of concepts involving fixed points and bifurcations in introductory differential equations courses. This study represents the spread of an outbreak from one end of a forest to the other. Numerical simulations are conducted using spectral methods.

Keywords
spruce budworm, steady states, traveling waves, stability
Mathematical Subject Classification 2010
Primary: 34B15, 35B32, 35B35, 35C07
Milestones
Received: 6 June 2016
Accepted: 21 August 2016
Published: 14 May 2017

Communicated by John Baxley
Authors
Hala Al-Khalil
Stanford University
Stanford, CA 94305
United States
Catherine Brennan
UC Santa Cruz
1156 High Street
Santa Cruz, CA 95064
United States
Robert Decker
Department of Mathematics
University of Hartford
200 Bloomfield Ave
West Hartford, CT 06117
United States
Aslihan Demirkaya
Department of Mathematics
University of Hartford
Dano Hall 210
200 Bloomfield Ave
West Hartford, CT 06117
United States
Jamie Nagode
Colorado State University
Fort Collins, CO 80523
United States