zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Modeling and analysis of peer-to-peer botnets. (English) Zbl 1253.68045
Summary: Peer-to-Peer (P2P) botnets have emerged as one of the most serious threats to Internet security. To effectively eliminate P2P botnets, we present two novel dynamical models to portray the process of formation of P2P botnets, one of which is called microlevel model, the other is called macrolevel model. Also, the stability of equilibria is investigated along with the analysis of how to prevent the P2P botnet. Furthermore, by analyzing the relationship between infection rate and the proportion of the hosts with countermeasures, we obtain the mathematical expressions of effective immune regions and depict their numerical simulations. Finally, numerical simulations verify the correctness of mathematical analysis. Our results can provide the guidance for security practitioners to defend and eliminate P2P botnet at a cost-effective way.
MSC:
68M11Internet topics
05C82Small world graphs, complex networks (graph theory)
68R10Graph theory in connection with computer science (including graph drawing)
Keywords:
P2P botnets