The Linear Spatial-Temporal Interaction Process and its Relation to 1/ω-Noise
提出一种基于增长-交互模型的谱方法，研究个体生长与距离依赖交互如何生成时空模式，并分析长程持久性及幂律谱噪声。
SUMMARY If we are to gain an understanding of the evolutionary processes which generate pattern then time cannot be ignored, since a purely spatial viewpoint disregards the fundamental generating mechanism of the underlying process. We therefore develop a spectral approach based on a general growth–interaction model; individuals grow at intrinsic rate λ, while two individuals a distance r apart interact at rate ar times their size difference. Special cases considered involve nearest neighbour, geometric, logarithmic and Cauchy-type dependence. A separate study is made of ‘long-term persistence‘; an autoregressive binomial weight structure is used to generate processes with power law spectra ωd. We examine the effect of arranging the general process on a ring of N sites, and then use this structure to simulate nearest neighbour and binomial interaction.