In this paper, we investigate the adaptive exponential synchronization in both the mean square and the almost sure senses for an array of $ {N}$ identical Markovian stochastic coupled neural… Click to show full abstract
In this paper, we investigate the adaptive exponential synchronization in both the mean square and the almost sure senses for an array of $ {N}$ identical Markovian stochastic coupled neural networks of neutral-type with time-varying delay and random coupling strength. The generalized Lyapunov theorem of the exponential stability in the mean square for the neutral stochastic Markov system with the time-varying delay is first established. The time-varying delay in the system is assumed to be a bounded measurable function. Then, sufficient conditions to guarantee the exponential synchronization in the mean square for the underlying system are developed under an adaptive feedback controller, which are given in terms of the $\mathcal {M}$ -matrix and the algebraic inequalities. Under the same conditions, the almost sure exponential synchronization is also presented. A numerical example is given to show the effectiveness and potential of the proposed theoretical results.
