Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Stability of the Periodic Solution of the Three Level Food Chain
  Model with Extinction of Top Predator   In this work, we revisit the classical Holling type II three species food
chain model from a different viewpoint. Two critical parameters {\lambda}1 and
{\lambda}2 dependent on all parameters are defined. The existence and local
stabilities of all equilibria can be reformulated by {\lambda}1 and {\lambda}2,
and the complete classifications of parameters and its corresponding dynamics
are given. Moreover, with the extinction of top-predator, there is an invariant
two dimensional subsystem containing the prey and the intermediate predator. We
prove the global stability of the boundary equilibrium in R3+ by differential
inequality as well as Butler-McGehee lemma if it is stable. Alternatively,
there is a unique limit cycle when the boundary equilibrium lost its stability,
and we also show the global stability of the limit cycle in R3+ by differential
inequality and computing the Floquet Multipliers. Finally, some interesting
numerical simulations, the chaotic and the bi-stability phenomena, are
presented numerically. A brief discussion and biological implications are also
given.

32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ