Asymptotical Behaviors of Nonautonomous Discrete Kolmogorov System with Time Lags

Asymptotical Behaviors of Nonautonomous Discrete Kolmogorov System with Time Lags

Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays

Yaoping Chen, Fengde Chen, and Zhong Li College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China Correspondence should be addressed to Fengde Chen, [email protected] Received 6 May 2008; Revised 8 September 2008; Accepted 22 November 2008 Recommended by Juan Jose Nieto We study the dynamic behaviors of a general discrete nonautonomous system of plankton allel...

Nonautonomous Kolmogorov Parabolic Equations with Unbounded Coefficients

We study a class of elliptic operators A with unbounded coefficients defined in I × R for some unbounded interval I ⊂ R. We prove that, for any s ∈ I, the Cauchy problem u(s, ·) = f ∈ Cb(R ) for the parabolic equation Dtu = Au admits a unique bounded classical solution u. This allows to associate an evolution family {G(t, s)} with A, in a natural way. We study the main properties of this evolut...

New Asymptotical Stability and Uniformly Asymptotical Stability Theorems for Nonautonomous Difference Equations

New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous differenc...

Chaos and Asymptotical Stability in Discrete-time Neural Networks

2 Abstract This paper aims to theoretically prove by applying Marotto’s Theorem that both transiently chaotic neural networks (TCNN) and discrete-time recurrent neural networks (DRNN) have chaotic structure. A significant property of TCNN and DRNN is that they have only one fixed point, when absolute values of the self-feedback connection weights in TCNN and the difference time in DRNN are suff...