Asymptotic Analysis of Linear and Interval Linear Fractional-Order Neutral Delay Differential Systems Described by the Caputo-Fabrizio Derivative

Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.

Bifurcation Behavior near T-B Point in Delay Differential Systems

In this paper, we investigate the description of T-B singularity and the bifurcation behavior near T-B point for delay differential systems with two parameters.

STABILITY OF DELAY DIFFERENTIAL SYSTEMS BY SEVERAL LIAPUNOV FUNCTIONS

In this paper, we develop a new technique to study the stability of differential systems with finite delay, where the components of the state variable can be divided into m groups (1 ≤ m ≤ l), correspondingly, m functionals Vj(j = 1, 2,'''m ) are adopted, each W involves one of the m groups. In this way, to construct the suitable functionals for a given system is much easier, and the obtained conditions are less restrictive

THE ALL-DELAY STABILITY OF DEGENERATE DIFFERENTIAL SYSTEMS WITH DELAY

In this paper,the all-delay stability of degenerate differential systems with delay is discussed.We come up with some new criteria for evaluating the all-delay stability of degenerate differential systems with delay and degenerate neutral differential systems with delay.Also,we give an example to illustrate the main results.

THE V-FUNCTIONAL METHOD FOR THE STABILITY OF DEGENERATE DIFFERENTIAL SYSTEMS WITH DELAYS

In this paper we establish V-functional criterion theorems for the stability of general autonomous degenerate differential systems with delay. Then for a kind of degenerate differential systems with delay-the mixed systems of difference differential systems with difference systems, we give a specific form of V-functional, a corresponding criterion theorem and examples. Finally, for the stability of two dimension degenerate differential systems with delay, we obtain. the necessary and sufficient condition for the existence of a kind of V-functional.

STABILITY OF TIME VARYING SINGULAR DIFFERENTIAL SYSTEMS WITH DELAY

In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solution and the sufficient conditions under which the considered system is stable and exponentially asymptotically stable. These results will be very useful to further research on Roust stability and control design of uncertain singular control systems with delay.

Global Exponential Stability of Variable Delay and Time－varying Measure Differential Systems with Impulse Effect

This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function with discontinuous derivative, some criteria of global exponential asymptotic stability for the system are established. An example is given to illustrate the applicability of results obtained.

Application of homotopy perturbation method to solve two models of delay differential equation systems

In this paper, two delay differential systems are considered, namely, a famous model from mathematical biology about the spread of HIV viruses in blood and the advanced Lorenz system from mathematical physics. We then apply the homotopy perturbation method （HPM） to find their approximate solutions. It turns out that the method gives rise to easily obtainable solutions. In addition, residual error functions of the solutions are graphed and it is shown that increasing the parameter n in the method improves the results in both cases.

Intelligent computing networks for nonlinear influenza-A epidemic model

The differential equations having delays take paramount interest in the research community due to their fundamental role to interpret and analyze the mathematical models arising in biological studies.This study deals with the exploitation of knack of artificial intelligence-based computing paradigm for numerical treatment of the functional delay differential systems that portray the dynamics of the nonlinear influenza-A epidemic model(IA-EM)by implementation of neural network backpropagation with Levenberg-Marquardt scheme(NNBLMS).The nonlinear IA-EM represented four classes of the population dynamics including susceptible,exposed,infectious and recovered individuals.The referenced datasets for NNBLMS are assembled by employing the Adams method for sufficient large number of scenarios of nonlinear IA-EM through the variation in the infection,turnover,disease associated death and recovery rates.The arbitrary selection of training,testing as well as validation samples of dataset are utilizing by designed NNBLMS to calculate the approximate numerical solutions of the nonlinear IA-EM develop a good agreement with the reference results.The proficiency,reliability and accuracy of the designed NNBLMS are further substantiated via exhaustive simulations-based outcomes in terms of mean square error,regression index and error histogram studies.