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How to secure the virtual environment in the cloud computing is a crucial issue since the cloud computing has been providing various services in many areas in the globe. The main aim of this paper is to investigate a delayed malware propagation model for cloud computing security. Time delay due to time interval that the infected virtual machines need to reinstall system and time delay due to the temporary immunization period of the protected virtual machines are introduced into the model. First, sufficient conditions for local stability and existence of Hopf bifurcation are derived by choosing different combinations of the two time delays as bifurcating parameter. Second, global exponential stability of the model is explored with the aid of linear matrix inequalities method. Finally, numerical simulations are carried out to illustrate that the obtained results and suggestions to ensure security of the cloud computing are given in the conclusion according to analyzing the dynamics of the proposed delayed malware propagation model for cloud computing security.

This study considers a model which incorporates delays, diffusion and toxicity in a phytoplankton–zooplankton system. Initially, we analyze the global existence, asymptotic behavior and persistence of the solution. We then analyze the equilibria’s local stability and investigate the non-delayed system’s bifurcation phenomena, including Turing and Hopf bifurcations and their combination. Subsequently, we explore the effects of delays on bifurcation and the global stability of the system using Lyapunov functional, focusing on Hopf and Turing–Hopf bifurcations. Finally, we present numerical simulations to validate the theoretical results and verify the emergence of various spatial patterns in the system.

Pine wilt disease is a destructive forest disease with strong infectivity, a wide spread range and high difficulty in prevention and control. Since controlling Monochamus alternatus, the vector of pine wood nematode (Bursaphelenchus xylophilus) can reduce the occurrence of pine wilt disease efficiently, the parasitic natural enemy of M. alternatus, Dastarcus helophoroides, is introduced in this paper. Considering the influence of parasitic time of D. helophoroides on the control effect, based on the mutualistic symbiosis and parasitic relationship among pine wood nematode, M. alternatus and D. heloporoides, this paper establishes a pine wood nematode prevention and control model with delay. Then, the stability of positive equilibrium and the existence of Hopf bifurcation are discussed. Besides, we obtain the normal form of Hopf bifurcation by applying the multiple time scales method. Finally, numerical simulations with two sets of meaningful parameters selected by means of statistical analysis are carried out to support the theoretical findings. Through the comparative analysis of numerical simulations, the factors affecting the control effect of pine wilt disease are obtained, and some suggestions are put forward for practical control in the forest.

In this paper, the dynamical behaviors of a new cytokine-enhanced HIV infection model with intracellular delay ${\tau }_1$, virus replication delay ${\tau }_2$ and immune response delay ${\tau }_3$ are investigated. The positivity and boundedness of all solutions for the model with non-negative initial values have been proved. Moreover, two important biological parameters, called the virus reproductive number $R_0$ and the antibody immune reproductive number $R_1$ are established. By constructing suitable Lyapunov functionals and using LaSalle’s invariance principle, the global dynamics of the equilibria is completely determined by $R_0$ and $R_1$. On the one hand, the results show that intracellular delay ${\tau }_1$, viral replication delay ${\tau }_2$ and immune response delay ${\tau }_3$ have no effect on the stability of $E_0$, $E_1$, and if ${\tau }_1\ge 0$, ${\tau }_2\ge 0$, ${\tau }_3=0$, the endemic equilibrium with the presence of antibody response $E_2$ is globally asymptotically stable. On the other hand, when ${\tau }_1\ge 0$, ${\tau }_2\ge 0$, ${\tau }_3>0$, numerical analysis confirms the theorems and suggests that time delay play a positive role in virus infection, with the increase of ${\tau }_3$, the dynamic behavior of the equilibrium $E_2$ will change as follows: locally asymptotically stable $\to$ unstable; Hopf bifurcation appears.

In this paper, we propose a stochastic cholera model that incorporates media coverage and two time delays driven by Lévy noise in order to deeply understand the propagation process of cholera in the real world, generalized nonlinear incidence rates ${\beta }_1(M)$ and ${\beta }_2(M)$ are also introduced. First, we discuss the existence and uniqueness of the global positive solution of the stochastic model by using the Lyapunov method. Moreover, the dynamic properties of stochastic solution around the disease-free and endemic equilibria are demonstrated. At last, we present numerical simulation results to reveal how Lévy jumps, time delays and media coverage affect the asymptotic properties of the stochastic model.

In this paper, some properties of the solutions for Nicholson’s blowflies system with nonlocal operator and delay are performed in heterogeneous environment. First of all, the existence and uniqueness of the positive steady-state solution are studied by Lyapunouv–Schmidt reduction method and implicit function theorem. Moreover, the asymptotic behaviors of trivial and nontrivial positive steady-state solutions to the system are also researched through the sub-supersolution method and iterative method. This paper ends with conclusion and discussion.

This paper presents some sufficient conditions for the existence and global exponential stability of the almost periodic solution for impulsive bi-directional associative memory neural networks with time-varying delays by using Lyapunov functional and Gronwall-Bellmans inequality technique. Comparing with known literatures, the results of this paper are new and they complement previously known results.

Based on the inequality analysis, matrix theory and spectral theory, a class of general periodic neural networks with delays and impulses is studied. Some sufficient conditions are established for the existence and globally exponential stability of a unique periodic solution. Furthermore, the results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.

The effect of delay feedback control and adaptive synchronization is studied near sub-critical Hopf bifurcation of a nonlinear dynamical system. Previously, these methods targeted the nonlinear systems near their chaotic regime but it is shown here that they are equally applicable near the branch of unstable solutions. The system is first analyzed from the view point of bifurcation, and the existence of Hopf bifurcation is established through normal form analysis. Hopf bifurcation can be either sub-critical or super-critical, and in the former case, unstable periodic orbits are formed. Our aim is to control them through a delay feedback approach so that the system stabilizes to its nearest stable periodic orbit. At the vicinity of the sub-critical Hopf point, adaptive synchronization is studied and the effect of the coupling parameter and the speed factor is analyzed in detail. Adaptive synchronization is also studied when the system is in the chaotic regime.

In this paper, topology monitoring of growing networks is studied. When some new nodes are added into a network, the topology of the network is changed, which needs to be monitored in many applications. Some auxiliary systems (network monitors) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied to designing such network monitors. Based on the Lyapunov function method via constructing a potential or energy function decreasing along any solution of the system, and the LaSalle's invariance principle, which is a generalization of the Lyapunov function method, some sufficient conditions for achieving topology monitoring are obtained. Illustrative examples are provided to demonstrate the effectiveness of the new method.

Here we show that for coupled-map systems, the length of the transient prior to synchronization is both dependent on the coupling strength and dynamics of connections: systems with fixed connections and with no self-coupling display quasi-instantaneous synchronization. Too strong tendency for synchronization would in terms of brain dynamics be expected to be a pathological case. We relate how the time to synchrony depends on coupling strength and connection dynamics to the latency between neuronal stimulation and conscious awareness. We suggest that this latency can be identified with the delay before a threshold level of synchrony is achieved between distinct regions within the brain, as suggested by recent empirical evidence, in which case the latency can easily be understood as the inevitable delay before such synchrony build-ups. This is demonstrated here through the study of simplistic coupled-map models.

In this paper, finite-time synchronization of dynamical networks coupled with complex-variable chaotic systems is investigated. According to Lyapunov function method and finite-time stability theory, both the dynamical networks without and with coupling delay are considered through designing proper finite-time controllers. Several sufficient conditions for finite-time synchronization are derived and verified to be effective by some numerical examples.

Motivated by the current delay in WTO negotiations, we consider a model of a bilateral trade agreement in the presence of asymmetric cross-border externalities. In this model, we show that both countries conflict in their preferred set of policy agendas and thus have incentives to delay their negotiations. We also find that the extent of delay depends on the level of transfer between them. These results imply an importance of bilateral compensation scheme between developing and developed countries in the current WTO negotiations so as to reduce the delays.

We study the phenomenon of spatial coherence resonance (SCR) on Hodgkin–Huxley (HH) neuronal networks that are characterized with information transmission delay. In particular, we examine the ability of additive Gaussian noise to optimally extract a particular spatial frequency of excitatory waves in diffusive and small-world networks on which information transmission amongst directly connected neurons is not instantaneous. On diffusively coupled HH networks, we find that for short delay lengths, there always exists an intermediate noise level by which the noise-induced spatial dynamics is maximally ordered, hence implying the possibility of SCR in the system. Importantly thereby, the noise level warranting optimally ordered excitatory waves increases linearly with the increasing delay time, suggesting that extremely long delays might nevertheless preclude the observation of SCR on diffusive networks. Moreover, we find that the small-world topology introduces another obstacle for the emergence of ordered spatial dynamics out of noise because the magnitude of SCR fades progressively as the fraction of rewired links increases, hence evidencing decoherence of noise-induced spatial dynamics on delayed small-world HH networks. Presented results thus provide insights that could facilitate the understanding of the joint impact of noise and information transmission delay on realistic neuronal networks.

We consider synchronization in networks of delay-coupled oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network, e.g., in-phase oscillation, splay or various cluster states. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase, coupling strength, and delay time such that a desired state can be selected from an otherwise multistable regime.

A projective synchronization of chaotic complex system was investigated. First, the cross projective synchronization (the real part and the imaginary part synchronize up to different scaling factors, respectively) in coupled partially linear complex nonlinear dynamic system was realized without adding any control term. Then, we investigated the substantial conditions of projective synchronization of chaotic complex systems on whole state variable with time delay. The adaptive controllers were designed. Moreover, numerical simulations were given to confirm the analytical results.

In virtue of identifying the influence of nodes, the spatial distance of rumor propagation is defined with the partition and clustering in the network. Considering the temporal and spatial propagation characteristics of rumors in online social networks, we establish a delayed rumor propagation model based on the graph theory and partial functional differential equations. Firstly, the unique existence and uniform boundedness of the nonnegative solution are explored. Secondly, we discuss the existence of positive equilibrium points sufficiently. Thirdly, stabilities of the rumor-free and rumor-spreading equilibrium points are investigated according to the linearization approach and Lyapunov function. Finally, we perform several numerical simulations to validate theoretical results and show the influence of time delay on rumor propagation. Experimental results further illustrate that taking forceful actions such as increasing the time delay in the rumor-spreading process can control rumor propagation due to the timely effectiveness of the information.

The epidemic often spreads along social networks and shows the effect of memorability on the outbreak. But the dynamic mechanism remains to be illustrated in the fractional-order epidemic system with a network. In this paper, Turing instability induced by the network and the memorability of the epidemic are investigated in a fractional-order epidemic model. A method is proposed to analyze the stability of the fractional-order model with a network through the Laplace transform. Meanwhile, the conditions of Turing instability and Hopf bifurcation are obtained to discuss the role of fractional order in the pattern selection and the Hopf bifurcation point. These results prove the fractional-order epidemic model may describe dynamical behavior more accurately than the integer epidemic model, which provides the bridge between Turing instability and the outbreak of infectious diseases. Also, the early warning area is discussed, which can be treated as a controlled area to avoid the spread of infectious diseases. Finally, the numerical simulation of the fractional-order system verifies the academic results is qualitatively consistent with the instances of COVID-19.

In this paper, the generalized projective synchronization of a class of delayed neural networks is investigated. Based on the Lyapunov stability theorem, a kind of controller is designed. The generalized projective synchronization of delayed neural networks can be achieved by using this kind of controller. Theoretical analysis and numerical simulations are provided to verify the feasibility and effectiveness of the proposed scheme.

In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results.