Nonlinear Partial Difference Equations for the Two-Dimensional Ising Model

1980 ◽  
Vol 45 (9) ◽  
pp. 675-678 ◽  
Author(s):  
Barry M. McCoy ◽  
Tai Tsun Wu
Keyword(s):  
Ising Model ◽  
Difference Equations ◽  
Two Dimensional ◽  
Partial Difference Equations ◽  
Partial Difference

scholarly journals Forms of Solutions for Some Two-Dimensional Systems of Rational Partial Recursion Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Tarek F. Ibrahim ◽  
A. Q. Khan
Keyword(s):  
Closed Form ◽  
Difference Equations ◽  
Mathematical Induction ◽  
Second Order ◽  
Two Dimensional ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Alternative Approach

In this paper, we offer the closed-form expressions of systems of second-order partial difference equations. We will utilize an alternative approach to verify the results by (odd-even) dual mathematical induction. We research and enforce the specific solutions of partial difference formulas and ordinary difference formulas as a straight effect.

Chaotic Dynamics of Partial Difference Equations with Polynomial Maps

2021 ◽  
Vol 31 (09) ◽  
pp. 2150133
Author(s):  
Haihong Guo ◽  
Wei Liang
Keyword(s):  
Dynamical Systems ◽  
Computer Simulations ◽  
Difference Equations ◽  
Chaotic Dynamics ◽  
Discrete Dynamical Systems ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Polynomial Maps ◽  
Expansion Theory ◽  
Theoretical Results

In this paper, chaotic dynamics of a class of partial difference equations are investigated. With the help of the coupled-expansion theory of general discrete dynamical systems, two chaotification schemes for partial difference equations with polynomial maps are established. These controlled equations are proved to be chaotic either in the sense of Li–Yorke or in the sense of both Li–Yorke and Devaney. One example is provided to illustrate the theoretical results with computer simulations for demonstration.

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