TY - JOUR
T1 - Period-doubling and Neimark–Sacker bifurcations in a larch budmoth population model
AU - De Silva, T. Mihiri M.
AU - Jang, Sophia R.J.
N1 - Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2017/10/3
Y1 - 2017/10/3
N2 - We investigate a discrete consumer-resource system based on a model originally proposed for studying the cyclic dynamics of the larch budmoth population in the Swiss Alps. It is shown that the moth population can persist indefinitely for all of the biologically feasible parameter values. Using intrinsic growth rate of the consumer population as a bifurcation parameter, we prove that the system can either undergo a period-doubling or a Neimark–Sacker bifurcation when the unique interior steady state loses its stability.
AB - We investigate a discrete consumer-resource system based on a model originally proposed for studying the cyclic dynamics of the larch budmoth population in the Swiss Alps. It is shown that the moth population can persist indefinitely for all of the biologically feasible parameter values. Using intrinsic growth rate of the consumer population as a bifurcation parameter, we prove that the system can either undergo a period-doubling or a Neimark–Sacker bifurcation when the unique interior steady state loses its stability.
KW - Neimark–Sacker bifurcation
KW - Uniform persistence
KW - center manifold
KW - period-doubling bifurcation
UR - http://www.scopus.com/inward/record.url?scp=85025842564&partnerID=8YFLogxK
U2 - 10.1080/10236198.2017.1354989
DO - 10.1080/10236198.2017.1354989
M3 - Article
AN - SCOPUS:85025842564
SN - 1023-6198
VL - 23
SP - 1619
EP - 1639
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 10
ER -