Global Existence and Exponential Stability of Convection

The existence and global exponential stability

Abstract By employing Schauder’s fixed point theorem and a non-Liapunov method (matrix theory, inequality analysis), we obtain some new criteria that ensure existence and global exponential stability of a periodic solution to a class of functional differential equations. Applying these criteria to a cellular neural network with time delays (delayed cellular neural network, DCNN) under a periodi...

Mildly dissipative nonlinear Timoshenko systems — global existence and exponential stability

Existence and Global Exponential Stability of Positive Almost Periodic Solutions for a Delayed Nicholson’s Blowflies Model

This paper concerns with a class of delayed Nicholson’s blowflies model with a nonlinear density-dependent mortality term. Under appropriate conditions, we establish some criteria to ensure that the solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give some examples and numerical simulations to illustrate our main results.

Existence and Global Exponential Stability of Periodic Solutions for General Neural Networks with Time-Varying Delays

By using the coincidence degree theorem and differential inequality techniques, sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general neural networks with time-varying including bounded and unbounded delays. Some known results are improved and some new results are obtained. An example is employed to illustrate our feasible results.

Existence and Exponential Stability of Almost Periodic Solutions for Cellular Neural Networks without Global Lipschitz Conditions

In this paper cellular neutral networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results o...