Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of intersections of trajectories of linear systems   Present article deals with trajectorial intersections in linear fractional
systems ('systems'). We propose a classification of intersections of
trajectories in three classes viz. trajectories intersecting at same
time(EIST), trajectories intersecting at distinct times(EIDT) and self
intersections of a trajectory. We prove a generalization of separation theorem
for the case of linear fractional systems. This result proves existence of
EIST. Based on the presence of EIST, systems are further classified in two
types; Type I and Type II systems, which are analyzed further for EIDT. Besides
constant solutions and limit-cycle behavior, a fractional trajectory can have
nodal or cuspoidal intersections with itself. We give a necessary and
sufficient condition for a trajectory to have such types of intersections.

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The categories of this paper are: math-ph
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph