Henson S M, Costantino R F, Cushing J M, Dennis B, Desharnais R A
Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA.
Bull Math Biol. 1999 Nov;61(6):1121-49. doi: 10.1006/bulm.1999.0136.
Mathematical models predict that a population which oscillates in the absence of time-dependent factors can develop multiple attracting final states in the advent of periodic forcing. A periodically-forced, stage-structured mathematical model predicted the transient and asymptotic behaviors of Tribolium (flour beetle) populations cultured in periodic habitats of fluctuating flour volume. Predictions included multiple (2-cycle) attractors, resonance and attenuation phenomena, and saddle influences. Stochasticity, combined with the deterministic effects of an unstable 'saddle cycle' separating the two stable cycles, is used to explain the observed transients and final states of the experimental cultures. In experimental regimes containing multiple attractors, the presence of unstable invariant sets, as well as stochasticity and the nature, location, and size of basins of attraction, are all central to the interpretation of data.
数学模型预测，在没有时间依赖因素的情况下振荡的种群，在受到周期性强迫时会发展出多个吸引性的最终状态。一个周期性强迫的、具有阶段结构的数学模型预测了在面粉体积波动的周期性栖息地中培养的赤拟谷盗（面粉甲虫）种群的瞬态和渐近行为。预测结果包括多个（双周期）吸引子、共振和衰减现象以及鞍点影响。随机性，再加上将两个稳定周期分开的不稳定“鞍周期”的确定性影响，被用来解释实验培养中观察到的瞬态和最终状态。在包含多个吸引子的实验条件下，不稳定不变集的存在、随机性以及吸引域的性质、位置和大小，都是数据解释的核心。
