Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Delay-induced homoclinic bifurcations in modified gradient bistable
  systems and their relevance to optimisation   Nonlinear dynamical systems with time delay are abundant in applications, but
are notoriously difficult to analyse and predict because delay-induced effects
strongly depend on the form of the nonlinearities involved, and on the exact
way the delay enters the system. We consider a special class of nonlinear
systems with delay obtained by taking a gradient dynamical system with a
two-well "potential" function and replacing the argument of the right-hand side
function with its delayed version. This choice of the system is motivated by
the relative ease of its graphical interpretation, and by its relevance to a
recent approach to use delay in finding the global minimum of a multi-well
function. Here, the simplest type of such systems is explored, for which we
hypothesise and verify the possibility to qualitatively predict the
delay-induced effects, such as a chain of homoclinic bifurcations one by one
eliminating local attractors and enabling the phase trajectory to spontaneously
visit vicinities of all local minima. The key phenomenon here is delay-induced
reorganisation of manifolds, which cease to serve as barriers between the local
minima after homoclinic bifurcations. Despite the general scenario being quite
universal in two-well potentials, the homoclinic bifurcation comes in various
versions depending on the fine features of the potential. Our results are a
pre-requisite for understanding general highly nonlinear multistable systems
with delay. They also reveal the mechanisms behind the possible role of delay
in optimisation.

31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat