Some results about a special nonlinear difference equation and uniqueness of difference polynomial

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.

Download Full-text

On the Asymptotic Stability of the Nonlinear Difference Equation System

Journal of Mathematical Sciences and Modelling ◽

10.33187/jmsm.887537 ◽

2021 ◽

pp. 65-71

Author(s):

Serbun Ufuk DEĞER ◽

Yaşar BOLAT

Keyword(s):

Asymptotic Stability ◽

Difference Equation ◽

Equation System ◽

Nonlinear Difference Equation

Download Full-text

Global Behavior of a Higher-Order Nonlinear Difference Equation with Many Arbitrary Multivariate Functions

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.140219.070519 ◽

2019 ◽

Vol 9 (4) ◽

pp. 643-650

Author(s):

Wen-Xiu Ma

Keyword(s):

Difference Equation ◽

Higher Order ◽

Nonlinear Difference Equation ◽

Global Behavior ◽

Multivariate Functions

Download Full-text

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

Open Mathematics ◽

10.1515/math-2018-0123 ◽

2018 ◽

Vol 16 (1) ◽

pp. 1435-1444 ◽

Cited By ~ 3

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.

Download Full-text