Abstract
In this paper, we focus on the problem of synchronization for chaotic neural networks with stochastic disturbances. Firstly, we provide a basic result that the systems including the drive system, response system, and error system have a unique solution on the whole time horizon. Based on this result, we design a new control law such that the response system can be synchronized with the drive chaotic system in finite time. Furthermore, we show that the settling time is independent of the initial data under some proper conditions, which hints that the fixed-time synchronization of chaotic neural networks can be realized by our proposed method. Finally, we give simulations to verify the theoretical analysis for our main results.
Highlights
In the last two decades, the chaotic systems have drawn considerable attention due to interesting features for secure communication
Motivated by the previous works on stability and synchronization for deterministic and stochastic systems, we will study the finite-time synchronization for chaotic neural networks disturbed by noise
Finite-time synchronization On the one hand, if the controller u1 is designed of the form u1(t) = –Γ e(t) – λ(t) η1 e(t) α + η2 e(t) β 1{e(t)}, (17)
Summary
In the last two decades, the chaotic systems have drawn considerable attention due to interesting features for secure communication. There are many research results on the stability of deterministic and stochastic systems [8,9,10, 13, 22]. (2020) 2020:669 deterministic systems, a Lyapunov-type theorem on finite-time stability was established by Bhat and Bernstein [1], but for the stochastic case, similar results were provided in [3, 23, 25].
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