Our goal is to match some dynamical aspects of biological systems with that of networks of coupled logistic maps. With these networks we generate sequences of iterates, convert them to symbol sequences by coarse-graining, and count the number of times combinations of symbols occur. Comparison of this with the number of times these combinations occur in experimental data—a sequence of interbeat intervals for example—is a measure of the fitness of each network to describe the target data. The most fit networks provide a cartoon that suggests a decomposition of the experimental data into a component that may be produced by a simple dynamical subsystem, and a residual component, the result of detailed, particular characteristics of the system that generated the target data. In the space of all network parameters, each point corresponds to a particular network. We construct a fitness landscape when we assign a fitness to each point. Because the parameters are distributed continuously over their ranges, and because fitnesses are estimated numerically, any plot of the landscape involves a finite sample of parameter values. We’ll investigate how the local landscape geometry changes when the array of sample parameters is refined, and use the landscape geometry to explore complex relations between local fitness maxima.

我们的目标是将生物系统的某些动态方面与耦合逻辑图网络的动态方面相匹配。使用这些网络，我们生成迭代序列，通过粗粒度将它们转换为符号序列，并计算符号组合出现的次数。将此与这些组合在实验数据中出现的次数（例如一系列节拍间隔）进行比较，可以衡量每个网络对描述目标数据的适应度。最适合的网络提供了一幅卡通画，建议将实验数据分解为一个可能由简单动态子系统产生的组件，以及一个残差组件，这是生成目标数据的系统的详细、特定特征的结果。在所有网络参数的空间中，每个点对应一个特定的网络。当我们为每个点分配一个适应度时，我们构建了一个适应度景观。因为参数在它们的范围内连续分布，并且因为适应度是用数值估计的，所以景观的任何图都涉及参数值的有限样本。我们将研究在细化样本参数数组时局部景观几何形状的变化，并使用景观几何形状来探索局部适应度最大值之间的复杂关系。