Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays

Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen‐Grossberg–type neural networks

“…Remark With the reduced‐order method, the researchers in other works studied the inertial NNs different from the method used in those works. Note that the research object is the second‐order inertial NNs; it may be more meaningful and reasonable to design second‐order response inertial NNs with control inputs other than the reduced‐order systems.…”

“…Recently, inertial NNs with delay have been widely investigated by many authors . Ke and Miao, studied the global exponential stability of inertial Cohen‐Grossberg NNs with time delays by constructing a proper variable substitution to transform the original system to first‐order differential equation.…”

“…Ke and Miao, studied the global exponential stability of inertial Cohen‐Grossberg NNs with time delays by constructing a proper variable substitution to transform the original system to first‐order differential equation. By the same idea, the authors studied several model of INNs. Therefore, in those existing paper, a common method is transforming the original INNs into the first‐order differential equations by choosing suitable variable substitutions.…”

Nonlinear output control scheme for general decay synchronization of delayed neural networks with inertial term

“…Sice the INN model belongs to second‐order differential equations, dynamical behaviors of INNs are more complex and more difficult to discuss. Therefore, the dynamic analysis of INNs, especially INNs with delays, received much more attention in the past few decays …”

“…Therefore, the dynamic analysis of INNs, especially INNs with delays, received much more attention in the past few decays. [6][7][8][9][10][11][12] It is well known that the synchronization is unique in nature and plays a vital role in various contexts, ranging from biological systems that include animal gates, descriptions of the heart, and fireflies in the forest to chemistry, nonlinear optics, and meteorology. 13 Since it was first proposed by Pecora and Carroll to synchronize two identical systems with two different initial values, 14 synchronization has been comprehensively studied over the past few decades due to its potential applications in a wide variety of areas, ranging from secure communications to pattern recognition, even to modeling the human brain's activity.…”