## Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

### Analytic solutions of nonlinear Cournot duopoly game.

Discrete Dynamics in Nature and Society

### Analytic Solutions of second order Nonlinear Difference Equations all of whose Eigenvalues are 1

Rendiconti del Seminario Matematico della Università di Padova

### Analytic solutions of a nonlinear two variables difference system whose eigenvalues are both 1

Annales Polonici Mathematici

For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where $X\left(x,y\right)=\lambda ₁x+\mu y+{\sum }_{i+j\ge 2}{c}_{ij}{x}^{i}{y}^{j}$, $Y\left(x,y\right)=\lambda ₂y+{\sum }_{i+j\ge 2}{d}_{ij}{x}^{i}{y}^{j}$ satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂| ≠ 1" or "μ...

Page 1