Index
absolutely continuous, 54, 233, 251, 256, 298, 317
definition, 364
accumulation point, 12
acyclic covering, 187
attract
a neighborhood of itself, 42, 177
attractor, 30
average Lyapunov function
strong, 354
weak, 350
Banach space, 16
bounded
set, 13
Butler-McGehee lemma, 182
Cauchy sequence, 16
chain transitive set, 181
chemostat, 142
closed operator, 385
closed set, 12, 25
closure, 12
compact
map, 58
set, 11
compact attractor, 30
connected, 38
dual attractor, 137
stable, 137
extinction attractor, 129
global, 37
local, of compact sets, 38
stable, 47
of a class of sets, 36
of a set, 32, 39
of an open set, 40
of bounded sets, 37, 43, 147
of compact sets, 37, 38
of neighborhoods of compact sets, 37, 41
of points, 37, 40
persistence attractor, 129
upper semicontinuity of, 184
completeness, 16
condensing map, 158
cone, 273
connected set, 33
connected space, 33
convergence, 10
convergence of sets, 29
cooperative system, 370
decreasing, 53
diameter, 13
dissipative
ρ-dissipative, 61
weakly ρ-dissipative, 62
distance
from point to set, 11
from set to set, 14
dual
attractor, 137
dual operator, 386
dual relation, 386
equilibrium, 23, 58
disease-free, 68
endemic, 45
fixed point, 23
flow, 18
flow-connected, 34
fluctuation method, 149, 366
403
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