On Global Asymptotic Stability of Second Order Nonlinear Differential Systems

2002 ◽  
Vol 81 (3) ◽  
pp. 681-703 ◽  
Author(s):  
Yan Ping ◽  
Jiang Jifa
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Second Order ◽  
Differential Systems ◽  
Nonlinear Differential Systems

Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 711-724
Author(s):  
Ivan Kiguradze
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Global Asymptotic Stability ◽  
Trivial Solution ◽  
Well Posedness ◽  
Bounded Solutions ◽  
Differential Systems ◽  
Nonlinear Differential Systems

Abstract For systems of nonlinear nonautonomous ordinary differential equations, the conditions, optimal in a certain sense, are established, which guarantee the solvability and well-posedness of the problem on bounded solutions, the vanishing at infinity of all bounded solutions and the global asymptotic stability of a trivial solution.

scholarly journals On the Global Asymptotic Stability of a Second-Order System of Difference Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Ibrahim Yalcinkaya
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
System Of Difference Equations ◽  
Initial Values

A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations where the parameter and the initial values (for .

scholarly journals Stability of Nonhyperbolic Equilibrium Solution of Second Order Nonlinear Rational Difference Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
S. Atawna ◽  
R. Abu-Saris ◽  
E. S. Ismail ◽  
I. Hashim
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Asymptotic Stability ◽  
Equilibrium Solution ◽  
Initial Conditions ◽  
Second Order ◽  
Real Numbers ◽  
Positive Real ◽  
Rational Difference Equation ◽  
Hyperbolic Equilibrium

This is a continuation part of our investigation in which the second order nonlinear rational difference equation xn+1=(α+βxn+γxn-1)/(A+Bxn+Cxn-1), n=0,1,2,…, where the parameters A≥0 and B, C, α, β, γ are positive real numbers and the initial conditions x-1, x0 are nonnegative real numbers such that A+Bx0+Cx-1>0, is considered. The first part handled the global asymptotic stability of the hyperbolic equilibrium solution of the equation. Our concentration in this part is on the global asymptotic stability of the nonhyperbolic equilibrium solution of the equation.

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