Stability analysis of delayed Hopfield Neural Networks with impulses via inequality techniques

Comparative analysis on Hopf bifurcation of integer‐order and fractional‐order two‐neuron neural networks with delay

“…ð12Þ Now, we shall analyze the distribution of the roots of Equation (12). Let iφ(φ > 0) be the root of Equation 12, then we have −φ 2 e iφθ + iϑ 1 φ + ϑ 2 e − iφθ = 0: ð13Þ…”

“…Abundant achievements have been constantly emerging. For instance, Alimi et al 11 discussed the finite-time and fixed-time synchronization issue for inertial neural networks with proportional delays; by applying inequality skills, Arbi et al 12 studied the stability for a class of delayed Hopfield neural networks with impulses; with the aid of matrix measure approach, Kumar and Das 13 obtained the exponential stability condition for delayed bidirectional associative memory (BAM) neural networks; applying Lyapunov-Krasovskii functional and linear matrix inequality, Syed Ali et al 14 established a novel delay-dependent condition to ensure the stochastic asymptotic stability of neutral-type Markovian-jumping delayed BAM neural networks; Popa 15 dealt with the global μ-stability of complex-valued BAM neural networks with leakage delay. For more concrete publications on these topics, one can see previous studies.…”

“…(i) All roots of Equation(12) have strictly negative real parts when θ 2 [0, θ 0 ). (ii) When θ = θ 0 , Equation (12) has a pair of imaginary roots ±iφ 0 , and all other roots have strictly negative real parts.…”

Dynamics of BAM neural networks with mixed delays and leakage time‐varying delays in the weighted pseudo–almost periodic on time‐space scales

“…In fact, it is natural and important that systems contain some information about the derivative of the past state to further describe and model the dynamics for such complex neural reactions. Many researchers have studied the dynamics of various classes of neutral‐type neural networks . Furthermore, in real world, the mixed time‐varying delays and leakage delay should be taken into account when modeling realistic neural networks.…”

“…Many researchers have studied the dynamics of various classes of neutral-type neural networks. 1,2,6,[34][35][36][37][38][39][40][41] Furthermore, in real world, the mixed time-varying delays and leakage delay should be taken into account when modeling realistic neural networks. In one study, 4 the authors establish some results about the existence and the global exponential stability of weighted pseudo-almost periodic solutions to linear dynamic equations on time scales and apply the results for a class of cellular neural networks with discrete delays on time scales.…”