The evolution equations mentioned in the title of this paper read as follows: where ℓ is the “discrete-time” independent variable taking integer values (ℓ = 0, 1, 2, … ), xn ≡ xn(ℓ) are the 2 dependent variables, , and the 2 functions P(n)(x1, x2), n = 1, 2, are 2 polynomials in the 2 dependent variables x1(ℓ) and x2(ℓ). The results reported in this paper have been obtained by an appropriate modification of a recently introduced technique to obtain analogous results in continuous-time t—in which case xn ≡ xn(t) and the above recursion relations are replaced by first-order ODEs. Their potential interest is due to the relevance of this kind of evolution equations in various applicative contexts.

中文翻译：

---

具有 2 个因变量在离散时间演化的可解系统，通过 2 个具有多项式右侧的非线性耦合一阶递归关系

本文标题中提到的演化方程如下： 其中 ℓ 是取整数值（ℓ = 0, 1, 2, … ）的“离散时间”自变量，xn ≡ xn(ℓ) 是 2变量, 和 2 个函数 P(n)(x1, x2), n = 1, 2 是 2 个因变量 x1(ℓ) 和 x2(ℓ) 中的 2 个多项式。本文报告的结果是通过对最近引入的技术进行适当修改而获得的，以获得连续时间 t 中的类似结果——在这种情况下，xn ≡ xn(t) 和上述递归关系被一阶 ODE 代替。他们的潜在兴趣是由于这种进化方程在各种应用环境中的相关性。