In this short paper, we point out that a single local stability controller can pin the complex network to a specified solution (or its equilibrium) of the coupled complex network. A rigorous mathematical proof is given, too.

This paper presents a study on the performance of the Hopfield neural network algorithm for the graph path search problem. Specifically, performance of the Hopfield network is studied from the dynamic systems stability perspective. Simulations of the time behavior of the neural network is augmented with exhaustive stability analysis of the equilibrium points of the network dynamics. The goal is...

We analyze the stability properties of an end-to-end congestion control scheme under fixed heterogeneous delays, and for general network topologies. The scheme analyzed is based on the congestion control game of [1], with the starting point being the unique Nash equilibrium of that game. We prove global stability of this solution (and hence of the congestion control algorithm) under a mild symm...

This paper provides sufficient conditions for global asymptotic stability and global exponential stability, which can be applied to nonlinear, large-scale, uncertain discrete-time systems. The conditions are derived by means of vector Lyapunov functions. The obtained results are applied to traffic networks for the derivation of sufficient conditions of global exponential stability of the uncong...

ABSTRACT. In this paper, the robust exponential stability problem is investigated for a class of uncertain Markovian jumping stochastic Cohen-Grossberg type bidirectional associative memory neural networks (CGBAMNN) with time-varying delays and reaction-diffusion terms. By using the Lyapunov stability theory and linear matrix inequality (LMI) technique, some robust stability conditions guarante...

in this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. we analyze the existence and stability of all possibleequilibria. numerical simulations reveal that anti-predator behaviour notonly makes the coexistence of the prey and predator po...

In this paper, we consider the direction and stability of time-delay induced Hopf bifurcation in a delayed predator-prey system with harvesting. We show that the positive equilibrium point is asymptotically stable in the absence of time delay, but loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold. Furthermore, using the norm form and the center manifo...

We calculate the Lebesgue–measures of the stability sets of Nashequilibria in pure coordination games. The results allow us to observe that the ordering induced by the Lebesgue–measure of stability sets upon strict Nashequilibria does not necessarily agree with the ordering induced by risk–dominance. Accordingly, an equilibrium selection theory based on the Lebesgue–measure of stability sets wo...

This paper considers the robust stability of neural networks with multiple delays. Based on Lyapunov stability theory and linear matrix inequality technique, some new delay independent conditions are derived to guarantee the global robust exponential stability of the equilibrium point. Furthermore, the obtained results are generalized to the interval neural networks and bidirectional associativ...

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be...