土壤生态系统耗散结构变异规律研究的理论与方法探讨

Theorectical and Methodological Discussion on the Research of Dissipative Structure of Soil Ecosystem

根据贝塔朗菲系统自生长的微分方程 ,可建立表征土壤生态系统动态变化的动力学方程 :dx/dt =(f-s)x-bx2 ,t为时间 ,x为土壤微生物数量 ,f为其繁殖系数 ,s为死亡系数 ,b为饱和系数 .其解 (1)x=x0 e(f-s)t,(2 )x =(f -s) /b.方程 (1)表明 ,如s>f,则当t→∞时 ,x→ 0 ,表明土壤生态系统处于热力学分支 ,将向退化的方向发展 ;方程 (2 )表明 ,如f>s ,其临界点x =(f -s) /b ,如x>x ,则表明土壤生态系统处于耗散结构分支 。

According to the equation of the system self growing, the nonlinear differential equation that can indicate the soil ecosystem dynamic change is suggested: d x /d t=(f-s)x-bx 2 , where, x -biological activity in soil ecosystem, t -time , f -coefficient of biological propagation, s -coefficient of biological death, b -coefficient of biological saturation The solution of the equation is follow as:(1) x=x 0 e (f-s)t ,(2) x * =(f-s)/b The equation (1) shows if s is larger than f , when time tends to ∞, x will tend to zero, and soil ecosystem locates at the branch of thermodynamics, and it will develop in the direction of degeneration The equation (2) shows if f is larger than s , critical point x * =(f-s)/b When x is larger than x * , the soil ecosystem locates at the branch of dissipative structure, and it will develop the direction of evolution