Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global dynamics of a novel delayed logistic equation arising from cell
  biology   The delayed logistic equation (also known as Hutchinson's equation or
Wright's equation) was originally introduced to explain oscillatory phenomena
in ecological dynamics. While it motivated the development of a large number of
mathematical tools in the study of nonlinear delay differential equations, it
also received criticism from modellers because of the lack of a mechanistic
biological derivation and interpretation. Here we propose a new delayed
logistic equation, which has clear biological underpinning coming from cell
population modelling. This nonlinear differential equation includes terms with
discrete and distributed delays. The global dynamics is completely described,
and it is proven that all feasible nontrivial solutions converge to the
positive equilibrium. The main tools of the proof rely on persistence theory,
comparison principles and an $L^2$-perturbation technique. Using local
invariant manifolds, a unique heteroclinic orbit is constructed that connects
the unstable zero and the stable positive equilibrium, and we show that these
three complete orbits constitute the global attractor of the system. Despite
global attractivity, the dynamics is not trivial as we can observe long-lasting
transient oscillatory patterns of various shapes. We also discuss the
biological implications of these findings and their relations to other logistic
type models of growth with delays.

16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ