TY - JOUR
T1 - Global stability for multi-species Lotka-Volterra cooperative systems
T2 - One hyper-connected mutualistic-species
AU - Vargas-De-Leon, Cruz
N1 - Publisher Copyright:
© 2015 World Scientific Publishing Company.
PY - 2015/5/12
Y1 - 2015/5/12
N2 - We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peripheral species around it, that is to say, one animal species (pollinators or dispersers) that interacts with several plant species (flowering plants or fruit trees), or several animal species that interact with one plant species. We derive a necessary and sufficient condition for the global asymptotic stability of the unique coexisting steady state of hyper-connected systems by means of novel Lyapunov functionals.
AB - We propose two models of one hyper-connected mutualistic-species described by delay differential equations of Lotka-Volterra type. An hyper-connected model comprises a central species interacting with a number of peripheral species around it, that is to say, one animal species (pollinators or dispersers) that interacts with several plant species (flowering plants or fruit trees), or several animal species that interact with one plant species. We derive a necessary and sufficient condition for the global asymptotic stability of the unique coexisting steady state of hyper-connected systems by means of novel Lyapunov functionals.
KW - Lotka-Volterra cooperative system
KW - Lyapunov functional
KW - discrete delays
KW - distributed delays
KW - global stability
UR - http://www.scopus.com/inward/record.url?scp=84941286484&partnerID=8YFLogxK
U2 - 10.1142/S1793524515500394
DO - 10.1142/S1793524515500394
M3 - Artículo
SN - 1793-5245
VL - 8
JO - International Journal of Biomathematics
JF - International Journal of Biomathematics
IS - 3
M1 - 1550039
ER -