On the stability of invariant sets of systems with impulse effect

New stability criterion of neural networks with leakage delays and impulses: a piecewise delay method

“…In the implementation of neural networks, it has also been shown that the presence of impulsive perturbations is likewise unavoidable (Fu et al 2005;Ignatyev 2008;Lakshmikantham et al 1989). So, the combination of impulsive perturbations and time delays in the leakage term can change the dynamic behavior of the neural network.…”

Existence and stability of almost periodic solutions for impulsive differential equations

“…Because of the needs of modern technology, such as simulation in physics, biology, populations dynamics, control theory, industrial robotics, etc., the study of impulsive differential equations attracts more and more researchers' interest, see [1][2][3][4][5][6][7][8]. There are many articles [9][10][11][12][13][14][15][16] about existence of solutions, periodic solutions and stability for impulsive differential equations. But, only a few articles [17,18] have studied the existence of almost periodic solutions to abstract impulsive differential equations in Banach space.…”

Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations

“…At the same time, the effect of impulse is also taken into account in researching the synchronization problem to reflect a more realistic dynamics [37][38][39]. By employing the method of impulsive delay differential inequality, several LMI-based conditions ensuring the exponential synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations are obtained, which are independent of time-varying delays.…”