Strictly cooperative systems with a first integral
Strictly cooperative systems with a first integral
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DOI：
10.1137/0518049
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发表时间：
1987-05
影响因子：
2
通讯作者：
J. Mierczynski
中科院分区：
文献类型：
--
作者：
J. Mierczynski
考虑微分方程组${{dx_i } / {dt}} = F_i（x_1，\cdots，x_n）$在n-空间的非负正交中满足以下假设：i）$F（0）= 0$; ii）如果$x_i < y_i $且$x_j = y_j $，则$F_k（x）< F_k（y）$，$k \ne i$; iii）F有一个正梯度的第一积分。我们证明了这样一个系统的每一个解决方案，要么收敛到一个平衡，或最终离开任何紧集。
We consider systems of differential equations ${{dx_i } / {dt}} = F_i (x_1 , \cdots ,x_n )$ in the nonnegative orthant in the n-space satisfying the following hypotheses: i) $F(0) = 0$; ii) if $x_i < y_i $ and $x_j = y_j $ for $j \ne i$ then $F_k (x) < F_k (y)$ for $k \ne i$; iii) F possesses a first integral with positive gradient. We prove that every solution to such a system either converges to an equilibrium or eventually leaves any compact set.