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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
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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
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Global asymptotic stability in a rational recursive sequence
Applied Mathematics and Computation, 2004 The global stability of the difference equation \[ x_{n}=\frac{a+bx_{n-1}+cx_{n-1}^2}{d-x_{n-2}}, \quad n=1,2,\dots \] where \(a,b\geq 0\) and \(c,d>0\) is studied. It is shown that one nonnegative equillibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive solution of the equation in ...
Xiaofan Yang 0001 +3 more
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Oscillation and global asymptotic stability of a neuronic equation with two delays [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2008 In this paper we study the oscillatory and global asymptotic stability of a single neuron model with two delays and a general activation function. New sufficient conditions for the oscillation and nonoscillation of the model are given.
Hassan A. El-Morshedy, B. M. Elmatary
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Global asymptotic stability of solutions of cubic stochastic difference equations [PDF]
Advances in Difference Equations, 2004 Global almost sure asymptotic stability of solutions of some nonlinear stochastic difference equations with cubic-type main part in their drift and diffusive part driven by square-integrable martingale differences is proven under appropriate conditions ...
Henri Schurz, Alexandra Rodkina
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Asymptotic behaviours of stochastic differential delay equations [PDF]
, 2005 Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper.
Shen, Yi +3 more
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Global asymptotic stability of complex-valued neural networks with additive time-varying delays. [PDF]
Cogn Neurodyn, 2017 Global asymptotic stability of complex-valued neural networks with additive time-varying ...
Subramanian K, Muthukumar P.
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Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching [PDF]
, 2008 The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching.
Yuan, Chenggui +4 more
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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
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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.
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