scholarly journals Global stability of periodic orbits of non-autonomous difference equations and population biology

2005 ◽  
Vol 208 (1) ◽  
pp. 258-273 ◽  
Author(s):  
Saber Elaydi ◽  
Robert J. Sacker
Keyword(s):  
Global Stability ◽  
Periodic Orbits ◽  
Difference Equations ◽  
Population Biology ◽  
Stability Of Periodic Orbits

scholarly journals EXISTENCE AND STABILITY OF PERIODIC ORBITS OF PERIODIC DIFFERENCE EQUATIONS WITH DELAYS

2008 ◽  
Vol 18 (01) ◽  
pp. 203-217 ◽  
Author(s):  
ZIYAD ALSHARAWI ◽  
JAMES ANGELOS ◽  
SABER ELAYDI
Keyword(s):  
Difference Equation ◽  
Periodic Orbits ◽  
Difference Equations ◽  
Asymptotically Stable ◽  
Stable Orbit ◽  
Globally Asymptotically Stable ◽  
Stability Of Periodic Orbits ◽  
Existence And Stability ◽  
Sharkovsky's Theorem ◽  
Positive Integers

In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xn = f(n - 1, xn-k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of gcd(p, k) nonautonomous p/gcd(p, k)-periodic difference equations. We give formulas for calculating the number of different periodic orbits under certain conditions. In addition, when p and k are relatively prime integers, we introduce what we call the pk-Sharkovsky's ordering of the positive integers, and extend Sharkovsky's theorem to periodic difference equations with delays. Finally, we characterize global stability and show that the period of a globally asymptotically stable orbit must be divisible by p.

Global stability and periodic orbits for two-patch predator-prey diffusion-delay models

1987 ◽  
Vol 85 (2) ◽  
pp. 153-183 ◽  
Author(s):  
Edoardo Beretta ◽  
Fortunata Solimano ◽  
Yasuhiro Takeuchi
Keyword(s):  
Global Stability ◽  
Periodic Orbits ◽  
Predator Prey ◽  
Delay Models
Sign in / Sign up

Export Citation Format

Share Document