Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite time Blow up in a population model with competitive interference
  and time delay   In the current manuscript, an attempt has been made to understand the
dynamics of a time-delayed predator-prey system with modified Leslie-Gower and
Beddington-DeAngelis type functional responses for large initial data. In
\cite{RK15}, we have seen that the model does possess globally bounded
solutions, for small initial conditions, under certain parametric restrictions.
Here, we show that actually solutions to this model system can blow-up in
finite time, for large initial condition, \emph{even} under the parametric
restrictions derived in \cite{RK15}. We prove blow-up in the delayed model, as
well as the non delayed model, providing sufficient conditions on the largeness
of data, required for finite time blow-up. Numerical simulations show, that
actually the initial data does not have to be very large, to induce blow-up.
The spatially explicit system is seen to possess Turing instability. We have
also studied Hopf-bifurcation direction in the spatial system, as well as
stability of the spatial Hopf-bifurcation using the central manifold theorem
and normal form theory.

33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex