The issue of mean-square delayed consensus of nonlinear multi-agent systems (NMASs) suffered from denial-of-service (DoS) attacks under Markov switching topologies and dynamic event-triggered control (DETC) is studied. Firstly, the networks among agents are inevitably attacked because the communication networks are open access. DoS attacks that are destructive, stealthy and easy to realize are considered. Secondly, DoS attacks can result in random changes of the communication topologies, which are assumed to be uncertain nonhomogeneous Markov switching (UNMS) topologies with partially unknown transition rates (TRs). Then, in order to reduce unnecessary signal transmission, the adaptive control law and DETC are adopted. The sufficient conditions of mean-square delayed consensus of NMASs in term of random analysis method and distributed control theory are explored. Finally, the exactness of the results and the effectiveness of the methods are validated by the example given.

The bounded consensus problem for a class of nonlinear multiagent systems with disturbances whose states are not measurable is achieved by the event-triggered impulsive mechanism. Here, the observer is designed to reconstruct the state of multiagent systems considering that this state is unmeasurable. The bounded disturbance term is assumed to be an unmeasurable dilated state component. Then, the dilated state observer is designed for antidisturbance treatment. Appropriate trigger conditions and Lyapunov functions are constructed based on the event-triggered impulsive control method, and sufficient conditions for multiagent systems are obtained to achieve bounded consensus. Zeno behavior is eliminated under the control strategy. Numerical tests are conducted to verify the validity of the control methods.

The normalized Laplacian plays an indispensable role in exploring the structural properties of irregular graphs. Let $L_{n}^{8,4}$ represents a linear octagonal-quadrilateral network. Then, by identifying the opposite lateral edges of $L_{n}^{8,4}$, we get the corresponding M\”{o}bius graph $MQ_{n}(8,4)$. In this paper, starting from the decomposition theorem of polynomials, we infer that the normalized Laplacian spectrum of $MQ_{n}(8,4)$ can be determined by the eigenvalues of two symmetric quasi-triangular matrices $\mathcal{L}_{A}$ and $\mathcal{L}_{S}$ of order $4n$. Nextly, owning to the relationship between the two matrix roots and the coefficients mentioned above, we derive the explicit expressions of the degree-Kirchhoff indices and the complexity of $MQ_{n}(8,4)$.

This paper aims to investigate the time fractional Keller-Segel system with a small parameter. After the fractional order traveling wave transformation, the heteroclinic orbit to the degenerate time fractional Keller-Segel system is demonstrated through the method of constructing a suitable invariant region. Moreover, the persistence of traveling waves in the system with a small parameter can be further illustrated. The results are mainly reliance on the application of geometric singular perturbation theory and Fredholm theorem, which are fundamental theoretical frameworks for dealing with problems of complexity and high dimensionality. Eventually, the asymptotic behavior is depicted by the asymptotic theory to illustrate the rate of decay for traveling waves.

This article specically deals with the asymptotic synchronization of non-identical complex dynamic fractional order networks with uncertainty. Initially, by using the Riemann-Liouville derivative, we developed a model for the general non-identical complex network, and based on the properties of fractional order calculus and the direct Lyapunov method in fractional order, we proposed that drive and response system if nonidentical complex networks ensuring asymp-totic synchronization by using neoteric control. Second, taking into account the uncertainties of non-identical complex networks in state matrices and evaluating theirrequirements forasymptotic synchronization. In addition, to explain the eectiveness of the proposed approach, two numerical simulations are given.

The stability and boundedness for delayed impulsive SDEs driven by fBm are studied in this paper. Two kinds of noises, i.e, additive fBm noise and mul-tiplicative fBm noise are both taken into consideration. By using stochastic Lyapunov technique and impulsive control theory, sufficient criteria for pth moment exponential stability and mean square ultimate boundedness are derived, for two kinds of fBm driven delayed impulsive SDEs, respectively. As application, the obtained results are used to do practical synchronization w.r.t. a class of chaotic systems, in which the response system is perturbed by additive fBm noises. Finally, A Chua chaotic oscillator is given to verify the validity and applicability of the derived results.

The objective of the present paper is to investigate the dynamics of Hepatitis B-type virus (HBV) infection through mathematical model. Distinct to the existing mathematical models on HBV, the present model considers the various factors such as immune impairment, the maximum number of T-cells (total carrying capacity), logistic growth term. Besides, for more accuracy, the role of antiretroviral therapies are also involved in the analysis. In addition, time delays are inevitable during the activation of immune response and during the antiretroviral therapy. Considering these factors while formulating the mathematical model which helps to gain insights into the disease progression. With the derived model, the qualitative analysis such as stability analysis, bifurcation analysis and stabilization analysis can be performed to investigate the performance of the model over the period of time. The significance of the model parameters are revealed through Hopf-type bifurcation analysis and the global stability analysis of the proposed model. With the help of dataset values that are extracted from the literature the efficiency of the derived theoretical results are explored.