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Synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time-varying delays. (English) Zbl 1198.60040

The paper investigates the synchronization of the nodes in a class of complex dynamical networks with Markovian jumping parameters and mixed type delays. The mixed type delays are composed of discrete and distributed delays, where the discrete time delay is assumed to be random and its probability distribution is known a priori.
By employing Lyapunov functionals, some properties of the Kronecker product and stochastic analysis techniques, the authors derive sufficient conditions for delay-dependant synchronization stability in the mean square. These conditions are written in terms of linear matrix inequalities, which can be conveniently solved by an appropriate software, such as the LMI toolbox in Matlab.
A numerical example is presented at the end of the paper, to illustrate the main results.

MSC:

60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60H30 Applications of stochastic analysis (to PDEs, etc.)

Software:

LMI toolbox; Matlab
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