Wikan A
Harstad College, Norway.
Math Biosci. 1997 Nov;146(1):37-62. doi: 10.1016/S0025-5564(97)00074-6.
The dynamic consequences of reproductive delay in Leslie matrix models with nonlinear survival probabilities p are analyzed. In consideration of two-age classes, proof is presented for a wide range of p functions that, outside the strongly resonant cases, the transfer from stability to instability goes through a supercritical Hopf bifurcation and, moreover, that the nonlinear development has a strong resemblance of three or four cycles, either exact or approximate. In three-age class models, the tendency toward four-periodical dynamics is shown to be even more pronounced, a qualitative finding that gradually disappears as we turn to the higher-dimensional cases. We also prove that for models of any dimension n > 1 theme are regions in parameter space where the equilibrium is unstable at its creation and we demonstrate that the dynamics in this age-class extinguishing case is 2k.n cyclic.
分析了具有非线性生存概率p的莱斯利矩阵模型中繁殖延迟的动态后果。考虑两个年龄组，针对广泛的p函数给出了证明，即在非强共振情况下，从稳定到不稳定的转变通过超临界霍普夫分岔发生，而且非线性发展与三个或四个周期有很强的相似性，无论是精确的还是近似的。在三个年龄组模型中，四周期动态的趋势更为明显，这一定性发现随着我们转向更高维情况而逐渐消失。我们还证明，对于任何维度n>1的模型，参数空间中存在平衡在创建时就不稳定的区域，并且我们证明在这种年龄组灭绝情况下的动态是2k.n循环的。
