Results 1 to 10 of about 5,973 (246)
Global asymptotic stability of nonlinear cascade systems [PDF]
Applied Mathematics Letters, 2002 Consider the nonlinear cascade system \((*)\) \(dx/dt = f(x,y)\), \(dy/dt = g(y),\) where \(f:\mathbb{R}^n \times \mathbb{R}^m \rightarrow \mathbb{R}^n\) and \(g: \mathbb{R}^m \rightarrow \mathbb{R}^m\) are assumed to be \(C^1\)-functions and to satisfy \(f(0,0)=0\), \(g(0)=0.\) The author gives a short proof of a known result on the global asymptotic ...
V Sundarapandian
exaly +4 more sources
Global Asymptotic Stability of a Rational System [PDF]
Abstract and Applied Analysis, 2014 The main goal of this paper is to investigate the global asymptotic behavior of the difference equation xn+1=β1xn/A1+yn, yn+1=β2xn+γ2yn/xn+yn, n=0,1,2,… with β1,β2,γ2,A1∈(0,∞) and the initial value (x0,y0)∈[0,∞)×[0,∞) such that x0+y0≠0.
Lin-Xia Hu, Xiu-Mei Jia
doaj +3 more sources
Global Asymptotic Stability of a Nonautonomous Difference Equation [PDF]
Journal of Applied Mathematics, 2014 We study the following nonautonomous difference equation: xn+1=(xnxn-1+pn)/(xn+xn-1), n=0,1,…, where pn>0 is a period-2 sequence and the initial values x-1,x0∈(0,∞).
Mehmet Gümüş, Özkan Öcalan
doaj +7 more sources
Global Asymptotic Stability in a Class of Difference Equations [PDF]
Advances in Difference Equations, 2008 We study the difference equation xn=[(f×g1+g2+h)/(g1+f×g2+h)](xn−1,…,xn−r), n=1,2,…, x1−r,…,x0>0, where f,g1,g2:(R+)r→R+ and h:(R+)r→[0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui ...
Jianqiu Cao +3 more
doaj +5 more sources
Global asymptotic stability in quadratic systems
Electronic Journal of Differential EquationsA classical problem in the qualitative theory of differential systems that is relevant for its applications, is to characterize the differential systems which are globally asymptotically stable, that is differential systems having a unique equilibrium point for which all their orbits, with the exception of the equilibrium point, tend in forward time ...
Jaume Llibre, Claudia Valls
doaj +4 more sources
Global asymptotic stability of a nonlinear recursive sequence
Applied Mathematics Letters, 2004 Using a ``semicycle analysis method'' developed by the authors, they prove that the positive equilibrium of the nonlinear difference equation \[ x_{n+1}=\frac{x_nx_{n-1}^b+x_{n-2}^b+a}{x_{n-1}^b+x_nx_{n-2}^b+a}, \quad n\geq 0 \] is globally asymptotically stable for parameters \(a\geq 0\), \(b>0\) and initial values \(x_{-2},x_{-1},x_0>0\).
Deming Zhu
exaly +3 more sources
GLOBAL ASYMPTOTIC STABILIZATION OF THE SPINNING TOP [PDF]
Optimal Control Applications and Methods, 1995 SUMMARYWe consider the problem of controlling a top to the sleeping motion using two different actuation schemes. For a fixed‐base top two actuators are assumed to provide forces at the centre of mass in inertially fixed directions, while for a cart‐mounted top two actuators are assumed to apply forces to the cart in inertially fixed directions.
Wan, Chih-Jian +2 more
openaire +3 more sources
Alexandria Engineering Journal, 2020 We consider an electrical RLC circuit in two-dimensional spaces described by a fractional-order derivative. We propose the qualitative properties of the proposed model. We analyze the local asymptotic stability and the global asymptotic stability for the
Ndolane Sene
doaj +1 more source
On Global Asymptotic Stability of Solutions of Differential Equations [PDF]
Transactions of the American Mathematical Society, 1962 and (1.3) H(x) is negative definite (for fixed x # 0), then x=0 is a globally asymptotically stable solution of (1.1); i.e., every solution x=x(t) or (1.1) exists for large t and x(t)->0 as too. Among the results of [4], which deals with the case n =2, is the following: if (1.4) x=0 is a locally asymptotically stable solution of (1.1) and (1.3) is ...
Hartman, P., Czeslaw, O.
openaire +2 more sources
Some results on cascade discrete-time systems
Discrete Dynamics in Nature and Society, 2006 We present sufficient conditions for global asymptotic stability of cascade discrete-time systems. Considering failure of the global asymptotic stability in some cascade systems, we give an estimate of the region of attraction of the systems.
Xiao-Ming Bai +2 more
doaj +2 more sources