Narrow Results

This research focuses on stabilization challenges of a Power System (PS) described by a delayed conformable fractional-order nonlinear model. We adopt the Polynomial Fitting Approximation Algorithm (PFAA) to approximate the cardinal sine function by a Square Of Polynomial (SOP). A polynomial representation is made for PS with different behaviors by dividing the operating range into $r$ regions and then calculating an SOP approximation for each region. Thus, the PS is characterized by $r$ distinct models, each applicable within its respective region. An Observer Based Control (OBC) is designed to stabilize the considered PS. The proposed result ensures the stabilization of the different $r$ models by satisfying sufficient conditions based on the sum-of-squares (SOS) approach.

Multifractal detrended cross-correlation analysis (MF-DXA) has been developed to detect the long-range power-law cross-correlation of two simultaneous series. However, the synchronization of underlying data can not be guaranteed integrated by a variety of factors. We artificially imbed a time delay in considered series and study its influence on the multifractal cross-correlation analysis. Time delay is found to affect the multifractal characterization, where a larger time delay causes a weaker multifractality. We also propose an alternative modification on MF-DXA to make the process more robust. The logarithmic return and volatility of Chinese stock indices show cross-correlation scaling behavior and strong multifractality by MF-DXA as well as singularity spectrum analysis.

Taking into account the quarantine for an infectious disease, a susceptible-exposed-infected-quarantined-recovery-susceptible (SEIQRS) epidemic model with time delay on the finite scale-free network is given. The basic reproduction number $R_0$, which is dependent not only on all kinds of transfer rates, but also on the topology of the network, is derived. By constructing the Lyapunov function, it is asserted that the disease-free equilibrium of system is locally asymptotically stable if $R_0<1$, moreover, disease-free equilibrium of system is globally asymptotically stable when $R_0<1$. In addition, the influence of network nodes on the spread of diseases is discussed. Finally, the theoretical results are verified by corresponding numerical simulation.

In this work, we study the norovirus (NoV) epidemic model with random perturbations and a time delay. First of all, the existence and uniqueness of the global positive solution are obtained. Then, we derive sufficient conditions for the extinction of the disease. Moreover, by establishing appropriate Lyapunov function, the existence of a stationary distribution is discussed. Some numerical simulations are given to illustrate our analytical results.

Time-delay and unavailability of system states bring extra difficulties to synchronization of chaotic systems. This paper investigates observer-based synchronization of time-delay complex-variable chaotic systems (CVCSs) with complex parameters. Differing from the existing works that considered time delay only in the linear term of some special CVCSs, the two cases of time delay in and out of nonlinear terms in general CVCSs are considered here, respectively. In addition, for the case that system states are not available for control, an observer-based output feedback control approach is developed to estimate the system states and guarantee the time-delay CVCSs to achieve synchronization. Moreover, by combining Lyapunov–Krasovskii function with linear matrix inequality in the complex field, two sufficient criteria are derived to ensure complete synchronization of time-delay CVCSs. Finally, a numerical example is presented to illustrate the theoretical results.

The main aim of this paper is to analyze a mathematical model for malware dissemination on wireless sensor networks with time delay. Local stability and exhibition of the Hopf bifurcation are explored by means of analysis of the distribution of roots of the consequential characteristic equation. Moreover, global exponential stability is established with the help of linear matrix inequality techniques. Furthermore, properties of the Hopf bifurcation such as the direction and stability are studied by utilizing the normal form theory and the center manifold theorem. Finally, a computer numerical simulation example is presented to certify the rationality of our obtained results.