Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution

1997 ◽  
Vol 49 (12) ◽  
pp. 1872-1890 ◽  
Author(s):  
A. M. Samoilenko ◽  
V. E. Slyusarchuk ◽  
V. V. Slyusarchuk
Keyword(s):  
Banach Space ◽  
Difference Equation ◽  
Quasiperiodic Solution ◽  
Nonlinear Difference Equation

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

scholarly journals Periodic and subharmonic solutions for a 2nth-order p-Laplacian difference equation containing both advances and retardations

2018 ◽  
Vol 16 (1) ◽  
pp. 1435-1444 ◽  
Author(s):  
Peng Mei ◽  
Zhan Zhou
Keyword(s):  
Difference Equation ◽  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Nonlinear Difference Equation ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Explicit Criteria

AbstractWe consider a 2nth-order nonlinear difference equation containing both many advances and retardations with p-Laplacian. Using the critical point theory, we obtain some new explicit criteria for the existence and multiplicity of periodic and subharmonic solutions. Our results generalize and improve some known related ones.

Sign in / Sign up

Export Citation Format

Share Document