A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with time-varying delays

Abstract

In this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed delay and stochastic noise are simultaneously taken into consideration. In order to guarantee the exponential stability of our considered recurrent neural networks, two distinct types of sufficient conditions are derived on the basis of the Lyapunov functional and coefficient of our given system and also to construct a Lyapunov function for a large scale system a novel graph-theoretic approach is considered, which is derived by utilizing the Lyapunov functional as well as graph theory. In this approach a global Lyapunov functional is constructed which is more related to the topological structure of the given system. We present a numerical example and simulation figures to show the effectiveness of our proposed work.

Green–Haar wavelets method for generalized fractional differential equations

“…and 3.00445 × 10 -7 1.25591 × 10 -7 1.99284 × 10 -8 0.3 1.09542 × 10 - 5 9.66989 × 10 -6 1.55214 × 10 -6 8.73622 × 10 -7 0.5 5.35004 × 10 - 5 3.25183 × 10 -5 1.55037 × 10 -5 6.56296 × 10 -6 0.7 2.80508 × 10 - 4 1.31354 × 10 -4 5.49232 × 10 -5 2.15731 × 10 -5 0.9 6.65574 × 10 - 4 3.15256 × 10 -4 1.11750 × 10 -4 2.89674 × 10 -5…”

“…The fractional operators in (4) and (5) represent Caputo and Caputo-Hadamard fractional derivative, respectively.…”

“…These applications of fractional calculus have been elaborated previously by several authors. In essence, fractional calculus has been deployed for modeling the transfer of heat in heterogeneous media [1], nonlinear oscillation of earthquakes [2], signal processing [3], neural networks [4][5][6], fluid dynamic traffic flow [7], electromagnetism [8], bioengineering [9], economics [10], anomalous diffusions and fractal-like nature [11,12]. For the qualitative analysis of fractional differential equations, we refer the reader to [1,2,[13][14][15] and the references therein.…”

Asymptotic behavior of Clifford-valued dynamic systems with D-operator on time scales

“…As well it is known, in biochemical tests of the dynamics of neural networks, the neuronal information may be transferred through chemical reactivity, resulting in a neutral type process. In the recent past, greater effort has been given to the exponential convergence, existence, and analysis of the stability of equilibrium point and PAP solutions for neutral type neural networks (NTNNs) [33][34][35][36][37]. Namely, all NTNNs models taken into account in the above references can be characterized as non-operator-based neutral functional differential equations.…”

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

“…In realistic engineering applications, humans continuously like to obtain synchronization in a finite convergence time, which is known as FTS. Moreover, time delays are inevitable in nearly all dynamical systems including neural network, chemical process, and nuclear reactors, which may lead to system oscillation, instability behaviors, and divergence because of the limited switching speed of amplifier circuits (see [44][45][46][47][48]). In recent decades, an increasing interest in the field of finite-time synchronization criterion of FONNs with time delays has attracted many scientific communities, which has given rise to some meaningful and significant outcomes (see [49][50][51]).…”