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The security of mobile wireless sensor networks has captivated extensive attention of researchers because of their wide range of applications and vulnerability to attacks caused by malware. In this paper, we investigate a delayed malware propagation model on mobile wireless sensor network incorporating nonlinear incidence rate, logistic growth rate and recovery rate. Local asymptotic stability of the endemic equilibrium and existence of Hopf bifurcation at crucial value of the time delay are analyzed. Then, properties of Hopf bifurcation are explored. Specifically, global exponential stability is investigated via linear matrix inequality. An example is presented finally to underline the effectiveness of findings in our paper numerically and graphically. [ABSTRACT FROM AUTHOR]

This paper focuses on the Hopf bifurcation of a fractional tri-neuron network with both leakage delay and communication delay under different fractional orders. By applying fractional Laplace transform, the stability theorem of linear autonomous system and Hopf bifurcation theorem, we obtain a class of asymptotic stability criterion of zero solution as well as delay-induced Hopf bifurcation conditions for the considered system. Simultaneously, the stability and Hopf bifurcation for tri-neuron network with single fractional order are also discussed as a special case of our proposed neural network model. Finally, a simulation example is given to illustrate the efficiency of the presented theoretical results in this paper. [ABSTRACT FROM AUTHOR]

In comparison with numerous available results with regard to bifurcations on account of fractional-order neural networks (FONNs) with the retarded delays, this paper is concerned with the stability and bifurcation of FONN with neutral delays. Delay-induced bifurcation results are firstly, procured and the bifurcation diagrams with respect to different delays are nicely plotted. Then it reveals that both time delay and fractional order have important effects in affecting the stability and bifurcation of the developed FONN. It further detects that FONN involving neutral delays can postpone the onset of bifurcations of the developed FONN compared with FONN with the retarded delays. It hints that neutral delays have a vital impact on the dynamics of FONNs in comparison with FONN with the retarded delays, which has outstanding performance in maintaining stability of FONNs. Eventually, numerical examples are addressed to check the availability of the developed results. The obtained criterion can be evaluated as an important contribution to the stability issue of the considered neural networks (NNs). [ABSTRACT FROM AUTHOR]

Smoking poses an enormous threat to public health in the globe and continues to be one of the main cause of health problems. In this paper, a delayed smoking model with reversion class is proposed. Local stability of the smoking equilibrium and Hopf bifurcation is analyzed by taking the time delay as the bifurcation parameter. In particular, global exponential stability is proved by using the linear matrix inequality method. The theoretical results obtained are validated numerically and graphically. [ABSTRACT FROM AUTHOR]

This paper researches the problem of bifurcation for a ring fractional-order neural network (FONN) with self-connection delay and communication delay. Self-connection delay is firstly regarded as a bifurcation parameter to examine the bifurcations of the developed FONN, and the critical values of bifurcations with respect to self-connection delay are derived. Second, communication delay is further taken as a bifurcation parameter to investigate the bifurcations of the designed FONN, and the stability zones and bifurcation points are determined. It reveals that FONN exhibits excellent stability performance when electing a lesser value of them, and the stability performance is devastated and Hopf bifurcation arises upon taking a larger one. Eventually, the efficiency of the developed theory is appraised on account of numerical verifications. [ABSTRACT FROM AUTHOR]

This paper lucubrates the bifurcations of a fractional-order bidirectional associative memory neural network (FOBAMNN) with leakage and communication delays. Firstly, leakage delay is taken as a bifurcation parameter to detect the bifurcations of the proposed neural network (NN). Leakage delay-induced bifurcation results are commendably established. Then communication delay is regarded as a bifurcation parameter to investigate the bifurcations of the developed FOBAMNN, and the stability interval and bifurcation point are derived. It reveals that the devised FOBAMNN possesses outstanding stability performance if selecting a lesser value of them, while the bifurcation emerges of FOBAMNN and eventually leads to performance deterioration with an outsize one. Besides, the influence of fractional order on the bifurcation points is carefully studied. It perceives that a proper fractional order can heighten the stability performance of the developed FOBAMNN. Ultimately, numerical simulations are exploited to underpin the developed theory. [ABSTRACT FROM AUTHOR]

This paper characterizes the stability and bifurcation of fractional-order ratio-dependent Holling–Tanner type model with fractional domain (0 , 2 ]. The stability intervals and bifurcation conditions of the developed model are attained by viewing different delays as bifurcation parameters. Then, two numerical examples are employed to corroborate the correctness of the theoretical analysis consisting of figuring out the bifurcation point and checking the veracity of the acquired bifurcation results via the plotted bifurcation diagrams. It revamps the deficiency of fractional-order model with unique delay. The procured results are instrumental in exploring the intrinsic convolution of predator–prey models. [ABSTRACT FROM AUTHOR]

This paper studies the problem of bifurcation for a fractional-order predator–prey system with two different delays by considering fractional interval (0 , 2 ]. Multiple delays-depended stability domains of the developed model are procured and the bifurcation points are exactly established by taking advantage of two different delays as bifurcation parameters, respectively. It detects that the stability performance can be extremely varied with the changes of control parameter upon one delay is established. System possesses excellent stability performance when choosing the smaller control parameter, and Hopf bifurcation emerges from system once control parameter passes through the critical values, which degrades the performance of the system. Numerical simulations are finally performed to check our theoretical analysis. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Global warming is becoming a big concern for the environment since it is causing serious and often unexpected impacts on species, affecting their abundance, genetic composition, behavior and survival. So, the modeling study is necessary to investigate the effects of global warming in predator–prey dynamics. This research paper analyzed the memory effect evaluated by Caputo fractional derivative on predator–prey interaction using an exponential fear function with a Holling-type II function in the presence of global warming effect on prey and predator species. It is assumed that the densities of prey and predator species decrease due to the increase of global warming. It is considered that both prey and predator species are contributing to the increase of global warming. Also, it is considered that global warming is increasing constantly and decreasing due to the natural decay rate. All possible equilibria of the system are determined, and the stability of the system around all equilibria points is investigated. Around the interior equilibrium point, the Hopf bifurcation is also theoretically and numerically studied. A number of numerical simulation results are presented to demonstrate the impacts of fear, fractional order and global warming on the behavior of the model. It is observed that the global warming effect on predator species may destabilize the system but ultimately the system may become stable. Again, it is obtained that the natural decay rate of global warming can stabilize the system initially but a higher decay rate may destabilized the system. It is also found that the fractional-order model is determined to be more stable than the integer-order model. [ABSTRACT FROM AUTHOR]

The anti-predator element because of fear from predator population in prey–predator models has an excellent significance and it is able to lessen the duplicate of prey population to a positive degree. In this paper, a delayed prey–predator model including fear effect and predator-taxis sensitivity is studied. Local stability and occurrence of Hopf bifurcation are analyzed by fixing the time delay as the bifurcating parameter. Then, a series of sufficient criteria for global stability is established by designing a suitable Lyapunov function. Furthermore, direction and stability of the Hopf bifurcation are studied. Lastly, numerical simulation outcomes are performed to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, to explore propagation dynamics of computer viruses over the Internet, a delayed SLBRS (susceptible–latent–breaking-out–recovering–susceptible) model of computer viruses considering horizontal and vertical dissemination over Internet is studied. The basic reproduction number at which computer viruses are prone to be extinct or continue to exist is calculated with the help of the next generation matrix method. By choosing the time delay because of processing time consumed to recover the breaking-out computers as bifurcation parameter, a series of sufficient criteria for experience of Hopf bifurcation are derived. Specially, optimal strategies to control dissemination of computer viruses over Internet are established. Finally, numerical simulations for certificating correctness of our theoretical findings are carried out. The findings show that the exhibition of Hopf bifurcation has an important impact on prediction and control of the propagation of computer viruses over the Internet. [ABSTRACT FROM AUTHOR]

In this paper, the sufficient conditions for the stability of the equilibrium to the fractional-order differential dynamical system with Caputo–Hadamard derivative are investigated. The existence of Hopf bifurcation in two-dimensional fractional dynamical system with a positive parameter is shown. Then, some numerical simulations are presented for a better understanding. [ABSTRACT FROM AUTHOR]

This paper highlights the stability and bifurcation of a fractional-order predator–prey model involving two delays. The critical values of delays with respect to Hopf bifurcation are exactly calculated for the developed model by taking two different delays as bifurcation parameters, respectively. Moreover, the effects of fractional order and additional delay on the bifurcation point are carefully explored. It detects that the stability performance is extremely strengthened by taking an appropriate fractional order and another delay. This hints that the onset of Hopf bifurcation can be advanced (lagged) with variations of their values. Numerical simulations are ultimately employed to check the correctness of the derived theoretical analysis. [ABSTRACT FROM AUTHOR]