A New Approach to Stability Analysis for Stochastic Hopfield Neural Networks With Time Delays

Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

“…In studies [31,32,35,37,42,[45][46][47]51] and [10], the activation functions are assumed to be in the real number field and quaternion field, respectively. In studies [30,33,36,38,39,41,43,44,48,49,53] and [14][15][16][17][18][19][20][21][22]26,29,34], the activation functions are assumed to meet the Lipschitz condition in the real field and quaternion field, respectively. Table 2 summarizes the review of existing work.…”

“…The delay phenomenon may reduce the convergence rate to equilibria of NNs and even cause considerable damage to the stability of systems. The delay phenomena of NN models have been examined in the literature, including fixed delays [30], variable delays [9][10][11][12][13][21][22][23][24][25][26][31][32][33][34][35][36], infinitely distributed delays [21,33,34,36], and neutral delays [12]. Uncertain interference factors are also unpreventable in NNs.…”

Adaptive event‐triggered output‐feedback control for p‐normal stochastic nonlinear systems with uncertain output function and time‐varying delays

“…Recalling that f i,k and g i,k are locally Lipschitz, one can deduce that there exists a unique solution defined on the maximally-extended-interval [0, T f ) for switched SNS (1).…”

“…As stated in References 17, 18, system (1) with p i < 1 (also called as low-order systems) represents a broad class of nonlinear systems which is continuous but completely non-differentiable, which is an important non-smooth counterpart of strict-feedback or high-order systems. In the presence of stochastic disturbances and signal delays, many practical systems can be modeled by the stochastic differential equation as (1), such as the liquid-level system with interaction. 19,20 Then the work 18,21 constructed a global state-feedback controller for low-order time-delay systems in deterministic and stochastic case, respectively.…”

“…As a result of the signal transmission or the system intrinsic characteristics, time‐delay is a pervasive phenomenon existing in many physical systems, such as networked control, 1,2 chemical reactors, 3 and so on. Time‐delay phenomenon may cause the deterioration of response performance or even instability, thus many efforts have been made to get rid of the negative influences.…”