TY - JOUR
T1 - Dynamics of a stoichiometric producer-grazer system with seasonal effects on light level
AU - Asik, Lale
AU - Kulik, Jackson
AU - Long, Kevin
AU - Peace, Angela
N1 - Publisher Copyright:
© 2019 Laser and Optoelectronics Progress.All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2019
Y1 - 2019
N2 - Many population systems are subject to seasonally varying environments. As a result, many species exhibit seasonal changes in their life-history parameters. It is quite natural to try to understand how seasonal forcing affects population dynamics subject to stoichiometric constraints, such as nutrient /light availability and food quality. Here, we use a variation of a stoichiometric Lotka-Volterra type model, known as the LKE model, as a case study, focusing on seasonal variation in the producer's light-dependent carrying capacity. Positivity and boundedness of model solutions are studied, as well as numerical explorations and bifurcations analyses. In the absence of seasonal effects, the LKE model suggests that the dynamics are either stable equilibrium or limit cycles. However, through bifurcation analysis we observe that seasonal forcing can lead to complicated population dynamics, including periodic and quasi-periodic solutions.
AB - Many population systems are subject to seasonally varying environments. As a result, many species exhibit seasonal changes in their life-history parameters. It is quite natural to try to understand how seasonal forcing affects population dynamics subject to stoichiometric constraints, such as nutrient /light availability and food quality. Here, we use a variation of a stoichiometric Lotka-Volterra type model, known as the LKE model, as a case study, focusing on seasonal variation in the producer's light-dependent carrying capacity. Positivity and boundedness of model solutions are studied, as well as numerical explorations and bifurcations analyses. In the absence of seasonal effects, the LKE model suggests that the dynamics are either stable equilibrium or limit cycles. However, through bifurcation analysis we observe that seasonal forcing can lead to complicated population dynamics, including periodic and quasi-periodic solutions.
KW - carrying capacity
KW - ecological stoichiometry
KW - predator-prey model
KW - quasi-periodic solution
KW - seasonal forcing
UR - http://www.scopus.com/inward/record.url?scp=85058797621&partnerID=8YFLogxK
U2 - 10.3934/mbe.2019023
DO - 10.3934/mbe.2019023
M3 - Article
C2 - 30674129
AN - SCOPUS:85058797621
VL - 16
SP - 501
EP - 515
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
SN - 1547-1063
IS - 1
ER -