一类三维Lotka-Volterra方程的讨论

Study on three-dimensional Lotka-Volterra equations

讨论一类三维Lotka Volterra方程 N1=N1(R-N1-N2) N2=N2(r-μN1-N3) N3=N3(-d+αN2),其中R,r,μ,d,α为正实值参数.给出方程出现周期解分岐现象的条件,并确定了在计算重要参数中有广泛应用的一个级数.

The aim of this paper is to investigate three-dimensianal Lotka-Volterra equations as follows:_1=N_1(R-N_1-N_2)_2=N_2(r-μN_1-N_3)_3=N_3(-d+αN_2).Where R, r,μ,d and αare all positive real-valued parameters. Our purpose is to obtain the condition of (bifurcation) phenomenon in periodic solution of equation. And we establish a series that plays a widely applicative role in calculating important parameters.