Memory sampled data control for switched-type neural networks and its application in image secure communications

Recently, many scholars have discovered that fractional calculus possess infinite memory and can better reflect the memory characteristics of neurons. Therefore, this paper studies the Hopf bifurcation of a fractional‐order network with short‐cut connections structure and self‐delay feedback. Firstly, we use the Laplace transform to obtain the characteristic equation of the model, which is the transcendental equation containing four times transcendental item. Secondly, by selecting the communication delay as the bifurcation parameter and the other delay as the constant in its stability interval, the conditions for the occurrence of Hopf bifurcation are established; the bifurcation diagrams are provided to ensure that the derived bifurcation findings are accurate. Thirdly, in the case of identical neurons, the crossing curves method is exploited to the fractional‐order functional function equation to extract the Hopf bifurcation curve. Finally, two numerical examples are employed to confirm the efficiency of the developed theoretical outcomes.

Section: Introductionmentioning

confidence: 99%

Dynamical complexity of a fractional‐order neural network with nonidentical delays: Stability and bifurcation curves

Mo,

Huang,

et al. 2024

“…A switched system contains a certain number of subsystems (modes), and a switching signal is used to manage the switching behavior between subsystems. This has drawn great interest due to its wide application in the fields of motor systems, circuits, mechanical systems, power electronics, air traffic control [43–63], and so forth. Switched NNs are NNs that have a switching signal controlling their parameters.…”

Section: Introductionmentioning

confidence: 99%

Robust passivity analysis for uncertain stochastic switched inertial neural networks with time‐varying delay under a new state‐dependent switching law

Nasira Banu,

Banupriya,

Dhanya

2024

This paper addresses the problems of passivity and robust passivity for a class of stochastic switched inertial neural networks (SSINNs) with time‐varying parametric uncertainties. First, the original inertial neural networks can be converted into first‐order differential systems using a suitable variable transformation approach. Moreover, by using a proper Lyapunov–Krasovskii functional (LKF) theory, Jensen's inequality, and the state‐dependent switching (SDS) law approach, several adequate criteria are derived in terms of linear matrix inequalities (LMIs) to ensure passivity and robust passivity analysis of SSINNs with parametric uncertainties and time‐varying delays. It is demonstrated that the developed SDS law may guarantee the passivity requirements of the above‐considered system made up of all unstable subnetworks. Furthermore, the gains are obtained by solving a set of LMIs that can be easily verified by some standard numerical packages. Ultimately, two examples with numerical simulations are provided to demonstrate the efficacy and feasibility of the suggested method.

“…A switched system is made up of several subsystems and a switching signal that controls its switching. It has received much interest due to its practical importance in power systems, circuits, air traffic control, mechanical systems, and various other domains [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Switched NNs are a kind of NNs that exhibits the special characteristics of network mode switching.…”

Section: Introductionmentioning

confidence: 99%

Robust stability of uncertain stochastic switched inertial neural networks with time‐varying delay using state‐dependent switching law

Banu¹,

Banupriya²,

Krishnasamy

et al. 2023

In this paper, the problem of robust stability analysis for a type of uncertain stochastic switched inertial neural networks (SSINNs) with time-varying delay is investigated. First, the original second-order system is converted into first-order differential equations using the variable transformation method. Next, some sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained using Lyapunov-Krasovskii functional (LKF), state-dependent switching (SDS) method, and Jensen's integral inequality for estimating integral inequalities so that the augmented system is robust, global, and asymptotically stable in the mean square for the uncertain SSINNs with time-varying delay. It is shown that the stability of the above considered system composed of all unstable subsystems can be achieved by using the SDS law. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed SDS law.