We study the asymptotic behaviour of the Bianchi type VI0 universes with a tilted γ-law perfect fluid. The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, γ = 6/5, there exists a bifurcation line which signals a transition of stabili...

ABSTRACT. We study impulsive Cohen-Grossberg neural networks with S-type distributed delays. This type of delays in the presence of impulses is more general than the usual types of delays studied in the literature. Using analysis techniques we prove the existence of a unique equilibrium point. By means of simple and efficient Lyapunov functions we present some sufficient conditions for the expo...

In this paper, the effects of refuges used by prey on a predator-prey interaction with a class of functional responses are studied by using the analytical approach. The refuges are considered as two types: a constant proportion of prey and a fixed number of prey using refuges. We will evaluate the effects with regard to the local stability of the interior equilibrium point, the values of the eq...

We present a new method of analyzing the dynamics of self-organizing neural networks with different time scales based on the theory of flow invariance. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global asymptotic stability of the ...

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present a general methodology to yield explicit constraints on the coupling strengths to ensure the stability of the equilibrium point. Two models of coupled excita...

A bounded rationality duopoly game with delay is formulated. Its dynamical evolution is analyzed. The existence of an economic equilibrium of the game is derived. The local stability analysis has been carried out. The analysis showed that firms using delayed bounded rationality have a higher chance of reaching a Nash equilibrium point. Numerical simulations were used to show bifurcation diagram...

In this paper, the problem of finite-time stabilization is developed for nonholonomic chained form systems with communication delay in the input. The finite-time control laws are presented by utilizing the switching control strategy and the theory of finite-time stability, which can make the states of the nonholonomic chained form systems to converge from any non-equilibrium state to the equili...

In this paper, a generalized neural network of Cohen-Grossberg type with both discrete time-varying and distributed unbounded delays is considered. Based on M-matrix theory, sufficient conditions are established to ensure the existence and global attractivity of an equilibrium point. The global exponential stability of the equilibrium is also addressed but for the model with bounded discrete ti...

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.