In this letter, we discuss delayed Cohen-Grossberg neural network models and investigate their global exponential stability of the equilibrium point for the systems. A set of sufficient conditions ensuring robust global exponential convergence of the Cohen-Grossberg neural networks with time delays are given.
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.
The Middle East Respiratory Syndrome (MERS) has been identified in 2012 and since then outbreaks have been reported in various localities in the Middle East and in other parts of the world. To help predict the possible dynamics of MERS, as well as ways to contain it, this paper develops a mathematical model for the disease. It has a compartmental structure similar to SARS models and is in the form of a coupled system of nonlinear ordinary differential equations (ODEs). The model predictions are fitted to data from the outbreaks in Riyadh (Saudi Arabia) during 2013-2016. The results reveal that MERS will eventually be contained in the city. However, the containment time and the severity of the outbreaks depend crucially on the contact coefficients and the isolation rate constant. When randomness is added to the model coefficients, the simulations show that the model is sensitive to the scaled contact rate among people and to the isolation rate. The model is analyzed using stability theory for ODEs and indicates that when using only isolation, the endemic steady state is locally stable and attracting. Numerical simulations with parameters estimated from the city of Riyadh illustrate the analytical results and the model behavior, which may have important implications for the disease containment in the city. Indeed, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. The model is general and may be used to analyze outbreaks in other parts of the Middle East and other areas.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.