In this paper, we study a new graph invariant named Resistance-Harary index, defined as RH(G) = Sigma({u,v}subset of v(G)) 1/r(G)(u,v) where r(G)(u, v) is the resistance distance between vertices u and v of a connected graph G. We establish that S-n(3) and P-n(3). are the graphs with the maximal and minimal Resistance-Harary index among all unicyclic graphs on n vertices, respectively.

For a nontrivial graph G, its first and second Zagreb coindices are defined as the sum of degree sum of of nonadjacent vertex pairs and the sum of degree product of nonadjacent vertices pairs, respectively. Motivated by the work in [1], we study Zagreb coindices of a new kind of composite graph, namely, double graph. For any given nontrivial graph, explicit formulas are given for the Zagreb coindices of its double graph and k-iterated double graph, respectively.

By applying the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg neural networks on time scales. Moreover an example is given to illustrate our results.

This paper deals with the existence, the boundedness and the asymptotic behavior of the positive solutions to a first order fuzzy Ricatti difference equationxn+1=A+xnB+xn,n=0,1,…where {xn} is a sequence of positive fuzzy numbers, A,B and the initial value x0 are positive fuzzy numbers. Moreover an example is given to demonstrate the effectiveness of the results obtained.

AbstractIn this short paper, we show that, with three exceptions, if the Wiener index of a connected graph of order $n$ is at most $(n+ 5)(n- 2)/ 2$, then it is traceable.

In this paper, we investigate the boundedness, persistence and global asymptotic stability of positive solutions of the system of two nonlinear difference equationsx(n+1) = A + x(n-m)/y(n), y(n+1) = B + y(n-m)/x(n), n = 0,1...,were A, B is an element of(0, infinity), x(i) is an element of(0, infinity), y(i) is an element of(0, infinity), i = -m, -m + 1,...,0.

In this paper, we investigate the boundedness, persistence and global asymptotic stability of positive solutions of the system of two nonlinear difference equations.

In this paper fuzzy bi-directional associative memory (BAM) neural networks with constant delays are considered. Some sufficient conditions for existence and global exponential stability of unique equilibrium point are established by using fixed point theorem and differential inequality techniques. The results obtained are easily checked to guarantee existence, uniqueness and global exponential stability of equilibrium point.

In this work, a class of fuzzy Cohen-Grossberg neural networks (FCGNNs) with time-varying delays and impulse are considered. Applying differential inequality techniques, some sufficient conditions for the existence, uniqueness and global exponential stability of equilibrium point for the addressed neural network are obtained. Moreover an example illustrates the effectiveness of obtained results.

By applying some analysis skills and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for a kind of fuzzy BAM neural networks on time scales. Moreover an example is given to illustrate our results. Copyright © 2013 Watam Press.

In this paper, by using the theory of topological degree, Lyapunov functional and analysis technique, the sufficient conditions which ensure the existence, uniqueness and global exponential stability of the equilibrium point for fuzzy bi-directional associative memory neural networks with distributed delays are obtained. The results remove the usual assumption that the activation functions are bounded. An example is given to illustrate the effectiveness and feasibility of results obtained.

In this paper, we study the dynamical behavior of positive solution for a system of a rational third-order difference equation where , ; . MSC:39A10.

The existence of solution to fuzzy differential equation du/dt=F(t,u),u(t0)=u0(u0∈En) is in-vestigated by using theory of topological degree.It is shown that there is at least a solution to this equa-tion under F(t,u) satisfying some conditions.

In this work, employing Lyapunov functional and elemental inequality (\(2ab \leqslant ra^2 + \tfrac{1}{r}b^2\), r > 0), some sufficient conditions are derived for the existence and uniqueness of periodic solution of fuzzy bidirectional associated memory (BAM) neural networks with variable delays. Some new and simple criteria are obtained to ensure global exponential stability of periodic solution, which are important in design and applications of fuzzy BAM neural networks.

Constructing a new Lyapunov functional and employing inequality technique, the existence, uniqueness, and global exponential stability of the periodic oscillatory solution are investigated for a class of fuzzy bidirectional associative memory (BAM) neural networks with distributed delays and diffusion. We obtained some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution. The results remove the usual assumption that the activation functions are differentiable. An example is provided to show the effectiveness of our results.

We study a class of fuzzy bidirectional associated memory (BAM) networks with periodic coefficients. Some sufficient conditions for the existence and global exponential stability of periodic solutions of such fuzzy BAM neural networks are established by using a continuation theorem based on the coincidence degree and the Lyapunov-function method. These sufficient conditions are easy to verify in pattern recognition and automatic control. Finally, an example is given to show the feasibility and efficiency of our results.

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation xn+1 = Axn + xn 1 B + xn 1 ; n = 0; 1; ; where (xn) is a sequence of positive fuzzy number, A;B are positive fuzzy numbers and the initial conditions x 1;x0 are positive fuzzy numbers.

In this paper, employing continuation theorem of the coincidence degree, and inequality technique, some sufficient conditions are derived to ensure global exponential stability and the existence of periodic solution for fuzzy cellular neural networks with time-varying delays. These results have important leading significance in the design and applications of globally stable neural networks. Moreover an example is given to illustrate the effectiveness and feasibility of results obtained.

In this paper, by employing continuation theorem of coincidence degree, and inequality technique, some sufficient conditions are derived to ensure the existence of periodic solution for fuzzy cellular neural networks with time-varying delays. These results have important leading significance in the design and applications of neural networks.

In this paper, an age structured predator-prey model with time delays is studied. The linear stability of the positive equilibrium and the existence of Hopf bifurcation with delay tau are investigated. The length of delay which preserves the stability of the positive equilibrium is calculated. The analytical findings are illustrated with numerical simulations. Finally, main conclusions are included.