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This research conducts a comprehensive analytical investigation into a stochastic SIR epidemic model that integrates nonlinear power functions and logistic growth dynamics. We examine the intricacies of model behavior, demonstrating its capability to produce a positive global solution. Utilizing precisely defined Lyapunov functions, we demonstrate the essential prerequisites for establishing the ergodicity of this particular model. Furthermore, the research deduces adequate criteria for predicting the eventual eradication of infectious diseases within this theoretical framework. Ultimately, we supplement the study with numerical simulations to elucidate and substantiate the analytical findings. This work contributes to comprehending epidemic systems with nuanced growth patterns and intricate disease transmission mechanisms, offering insights into real-world epidemic potential behaviors and outcomes.

In this paper, SIR model with feedback control has been considered. By constructing the Lyapunov function, using the Routh–Hurwitz criterion and the positive definite quadratic form theory, some sufficient conditions have been obtained, and some well-known results have been generalized. It is worth mentioning that if the feedback control variables have an inhibitory effect on the susceptible population and the infected population, the number of basic regeneration of the disease will be reduced. The reduction depends only on the control of the susceptible population, but not on the control of the infected population. This is a very interesting conclusion.

In this paper, we propose a Zika transmission model which considers human-to-human sexual transmission, the extrinsic incubation period of mosquitoes, and the vector-bias effect. Firstly, the explicit expression of the basic reproduction number $R_0$ is given by using the next-generation operator method, and the global dynamics of the model are established by taking $R_0$ as the threshold condition, that is, if $R_0\le 1$, the disease-free equilibrium is globally asymptotically stable, if $R_0>1$, the model has a unique endemic equilibrium that is locally asymptotically stable and the disease persists. And when we ignore the vector-bias effect, the global asymptotic stability of the endemic equilibrium is proved by constructing a Lyapunov function. Then, we select the reported epidemic data from Brazil for fitting, which verifies the obtained theoretical results. Meanwhile, we study the impact of human-to-human sexual transmission rate and mosquito-to-human transmission rate on the spread and prevalence of Zika. In addition, we calculate the sensitivity indices of $R_0$ to the model parameters and provide effective measures to control Zika transmission. The simulation results indicate that extending the extrinsic incubation period of mosquitoes is beneficial for disease control while ignoring the vector-bias effect will underestimate the risk of Zika transmission.

In this paper, we study an SS_vEIQR model with nonlinear contact rate, isolation rate and vaccination rate driven by media coverage. First, the basic reproduction number $R_0$ is derived. Then, the threshold dynamics of the disease are obtained in terms of $R_0$: when $R_0\le 1$, the global stability of the disease-free equilibrium is obtained by constructing an appropriate Lyapunov function; when $R_0>1$, the sufficient conditions to prove the globally stability of endemic equilibrium are obtained by applying the geometric method into the four-dimensional system, which needs to estimate the Lozinski$ǐ$ measure of a $6\times 6$ matrix. Further, we conduct some numerical simulations to validate our theoretical results, and analyze the impact of media coverage on disease transmission, the results show that media coverage could effectively suppress the spread of the disease and reduce the number of infected individuals. Finally, through the sensitivity analysis of $R_0$, we obtain some measures to control the spread of the disease, such as reducing contact, strengthening isolation and vaccination.

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 view of the harm of heroin to human and society, the use and spread of heroin have been regarded as an epidemic, it is urgent for us to study and analyze the dynamical behavior of heroin epidemic model. Therefore, in this paper, we will investigate a stochastic heroin epidemic model with distributed delay. By constructing some suitable Lyapunov functions, we establish sufficient condition for the existence of a stationary distribution $\pi (\cdot )$ for the stochastic heroin epidemic model with distributed delay. Then, we analyze the theoretical results and give some suggestions to control the spread of heroin’s infectious diseases.

The susceptible population is categorized into two cohorts in proportion, and a network-based SEIR model is established to examine how self-protection awareness affects disease propagation. From the perspective of media reports and information dissemination among people, we carefully capture the enhancement of individuals’ awareness of self-protection amid the disease outbreak. The basic reproduction number $R_0$ is derived through the application of spectral analysis. We demonstrate the unique existence of the positive equilibrium, and then the stability of the two equilibria is determined by developing different Lyapunov functions. Sensitivity analysis determines the importance of parameters for $R_0$. Our numerical simulations suggest that decreasing the proportion of unconscious susceptible people in the input population and strengthening self-protection awareness can effectively curb the expansion of infection.

In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability criterion imposes constraints on the feedback matrices independently of the delay parameters. The result is compared with some previous works. Furthermore, the condition may be less restrictive in the case that the activation functions are hyperbolic tangent.

In this paper, the problem of global robust stability for shunting inhibitory cellular neural networks (SICNNs) is studied. A sufficient condition guaranteeing the network's global robust stability is established. The result can easily be used to verify globally robust stable networks. An example is given to illustrate that the conditions of our results are feasible.

In this paper a nonholonomic mobile robot with completely unknown dynamics is discussed. A mathematical model has been considered and an efficient neural network is developed, which ensures guaranteed tracking performance leading to stability of the system. The neural network assumes a single layer structure, by taking advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot dynamic parameters. No assumptions relating to the boundedness is placed on the unmodeled disturbances. It is capable of generating real-time smooth and continuous velocity control signals that drive the mobile robot to follow the desired trajectories. The proposed approach resolves speed jump problem existing in some previous tracking controllers. Further, this neural network does not require offline training procedures. Lyapunov theory has been used to prove system stability. The practicality and effectiveness of the proposed tracking controller are demonstrated by simulation and comparison results.

In this paper a hopping robot motion with offset mass is discussed. A mathematical model has been considered and an efficient single layered neural network has been developed to suit to the dynamics of the hopping robot, which ensures guaranteed tracking performance leading to the stability of the otherwise unstable system. The neural network takes advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot parameters. Time delays in the control mechanism play a vital role in the motion of hopping robots. The present work also enables us to estimate the maximum time delay admissible with out losing the guaranteed tracking performance. Further this neural network does not require offline training procedures. The salient features are highlighted by appropriate simulations.

The well known Cohen-Grossberg network is modified to include second order neural interconnections and also to have a learning component. Sufficient conditions are obtained for the existence of a globally exponentially stable equilibrium. The model provides a two-fold generalization of the Cohen-Grossberg network in the sense if one removes the learning component, then one gets a network with second order synaptic interactions; if both the learning component and the second order interactions are removed, then the model reduces to the standard Cohen-Grossberg network.

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference system of Hopfield neural networks in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result is applied to obtain new asymptotic stability condition for some class of delay-difference system such as delay-difference system of Hopfield neural networks with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational purposes.

In this paper, we present a neural adaptive control scheme for active vibration suppression of a composite aircraft fin tip. The mathematical model of a composite aircraft fin tip is derived using the finite element approach. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes very accurately. Piezo-electric actuators and sensors are placed at optimal locations such that the vibration suppression is a maximum. Model-reference direct adaptive neural network control scheme is proposed to force the vibration level within the minimum acceptable limit. In this scheme, Gaussian neural network with linear filters is used to approximate the inverse dynamics of the system and the parameters of the neural controller are estimated using Lyapunov based update law. In order to reduce the computational burden, which is critical for real-time applications, the number of hidden neurons is also estimated in the proposed scheme. The global asymptotic stability of the overall system is ensured using the principles of Lyapunov approach. Simulation studies are carried-out using sinusoidal force functions of varying frequency. Experimental results show that the proposed neural adaptive control scheme is capable of providing significant vibration suppression in the multiple bending modes of interest. The performance of the proposed scheme is better than the H_∞ control scheme.

In this paper, the finite-time outer synchronization between two complex dynamical networks with on–off coupling is investigated. By using suitable on–off controllers, sufficient conditions for finite-time outer synchronization are derived based on the Lyapunov function and the finite-time differential inequality method. The theoretical results imply that the two networks will achieve finite-time outer synchronization for fixed on–off rate if the control coupling strength is large enough. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.

This paper presents calculations of the rate constant for the unimolecular isomerization of cyclobutanone using the theory of Gray and Rice as extended by Zhao and Rice. Such calculations are also carried out from classical trajectory and from local Lyapunov function analysis. The results of the calculations as a function of energy are compared, and the agreement is found to be uniformly good. The present approach is considered as a computationally feasible alternative to Davis' turnstile approach to the calculations of intramolecular energy transfer.

This paper studies the fluid model of a special kind of multi-type queueing network with type priority. The fluid of the same type in the same station is operated under last buffer first served (LBFS) policy. The stability of this kind of fluid model is proved via the Lyapunov function.

For smooth convex optimization problems, the optimal convergence rate of first-order algorithm is $O(1/k^2)$ in theory. This paper proposes three improved accelerated gradient algorithms with the gradient information at the latest point. For the step size, to avoid using the global Lipschitz constant and make the algorithm converge faster, new adaptive line search strategies are adopted. By constructing a descent Lyapunov function, we prove that the proposed algorithms can preserve the convergence rate of $O(1/k^2)$. Numerical experiments demonstrate that our algorithms perform better than some existing algorithms which have optimal convergence rate.

This work deals with dynamical system analysis of Holographic Dark Energy (HDE) cosmological model with different infra-red (IR)-cutoff. By suitable transformation of variables, the Einstein field equations are converted to an autonomous system. The critical points are determined and the stability of the equilibrium points are examined by Center Manifold Theory and Lyapunov function method. Possible bifurcation scenarios have also been explained.

Secure communications via chaotic synchronization is demonstrated in this literature. At first we have designed a feedback controller for chaotic synchronization utilizing the Lyapunov stability theory for cascade-connected systems.The method has been applied successfully to make two identical systems globally asymptotically synchronized. The result of numerical simulations are given to validate the effectiveness of this method. Then we have discussed a new method of cryptography for this coupled system which is very simple to implement and effective.