Abstract
In this work, we mainly focus on uncertain delayed neural network system with inertial term. Here, the existence, uniqueness, and exponential stability of inertial neural networks are derived without shifting the second order differential system into first order through substituting variables. Initially, we construct a proper Lyapunov–Krasovskii functional to investigate the stability of novel uncertain delayed inertial neural networks, which is different from the classical Lyapunov functional approach. By utilizing the Kirchhoff’s matrix tree theorem, Cauchy–Schwartz inequality, homeomorphism theorem, and some inequality techniques, the necessary and sufficient conditions are derived for the designed framework. Subsequently, to exhibit the strength of this outcome, we framed a quantitative example.
Highlights
IntroductionBecause of the fruitful applications in various domains such as gesture recognition [1], image quality enhancement [2], secure communication [3], face detection [4], image compression [5] and medical image processing [6], the dynamical behaviour of different kinds of neural networks (NNs), namely, Cohen-Grossberg neural networks (CGNNs) [7], recurrent neural networks (RNNs) [8, 9], Hopfield neural networks [10], bidirectional associative memory neural networks (BAMNNs) [11], and chaotic neural networks (CNNs) [12], have been studied widely
Because of the finite propagation velocity, time delays are unavoidable in signal transmission of neural networks, which may lead the unwanted dynamical responds such as chaotic and bifurcation
The time-delays occur due to Mathematical Problems in Engineering the propagation time of neurotransmitters forming presynaptic neurons to postsynaptic neurons. e time delays are occurring in constant manner [14] and according to the number of parallel pathways with different lengths and sizes of the axon; it may be classified into various kinds such as discrete [15, 16], distributed, and mixed delays [17,18,19]
Summary
Because of the fruitful applications in various domains such as gesture recognition [1], image quality enhancement [2], secure communication [3], face detection [4], image compression [5] and medical image processing [6], the dynamical behaviour of different kinds of neural networks (NNs), namely, Cohen-Grossberg neural networks (CGNNs) [7], recurrent neural networks (RNNs) [8, 9], Hopfield neural networks [10], bidirectional associative memory neural networks (BAMNNs) [11], and chaotic neural networks (CNNs) [12], have been studied widely. The exponential stability of CNNs with proportional delay was investigated by utilizing the matrix theory and Lyapunov theory. The convergence analysis of INNs has been focused by lot of research scientists, for instance by utilizing the Lyapunov functional method, inequality techniques, and analytical method, the global Lagrange stability of INNs with discrete and distributed time-varying delays [31, 32]. Various kinds of Lyapunov functionals are applied in the stability of neural networks system, for instances [41] Kong et al studied the synchronization INNs on the basis of indefinite Lyapunov–Krasovskii functional method, by utilizing the new augmented Lyapunov–Krasovskii functional. (i) In this work, we investigate the exponential stability results of inertial neural networks along with the existence of uncertainty and distributed and proportional time-varying delay.
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